Hex 3F To Decimal? The 25 Correct Answer

Hexadecimal to Decimal Converter

To use this online hex to decimal converter tool, enter a hex value like 1E in the left box below and then click the Convert button. You can convert up to 16 hexadecimal characters (max. value 7fffffffffffffff) into decimal numbers.

Hex Value (max 7ffffffffffffffff) Convert Decimal Value Swap Conversion: Decimal to Hex

Converting from hex to decimal gives base numbers

How to calculate hexadecimal to decimal

Hex is a base 16 number and decimal is a base 10 number. We need to know the decimal equivalent of each digit of a hexadecimal number. See bottom of page to check hex-decimal chart.

Here are the steps to convert hex to decimal:

Get the decimal equivalent of Hex from the table.

Multiply each digit by 16 to the power of the digit position.

(zero based, 7DE: E position is 0, D position is 1 and the 7 position is 2)

(zero based, 7DE: E position is 0, D position is 1 and the 7 position is 2) Sum all the multipliers.

Here is an example:

7DE is a hexadecimal number 7DE = (7 * 162) + (13 * 161) + (14 * 160) 7DE = (7 * 256) + (13 * 16) + (14 * 1) 7DE = 1792 + 208 + 14 7DE = 2014 (in decimal)

Hexadecimal system (Hex system)

The hexadecimal system (Hex for short) uses the number 16 as the base (radix). It uses 16 symbols as the base-16 number system. These are the 10 decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the first six letters of the English alphabet (A, B, C, D, E, F). The letters are used because the values ​​10, 11, 12, 13, 14, and 15 must each be represented in a single symbol.

Hex is used in mathematics and information technology as a friendlier way to represent binary numbers. Each hexadecimal digit represents four binary digits; Therefore Hex is a language to write binary in abbreviated form.

Four binary digits (also called nibbles) make half a byte. This means that a byte can carry binary values ​​from 0000 0000 to 1111 1111. In hex, these can be presented in a friendlier way and range from 00 to FF.

In HTML programming, colors can be represented by a 6-digit hexadecimal number: FFFFFF stands for white, while 000000 stands for black.

decimal system

The decimal number system is the most used and the standard system in everyday life. It uses the number 10 as its base (radix). Therefore, it has 10 symbols: the numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

One of the oldest number systems known, the decimal number system was used by many ancient civilizations. The difficulty of representing very large numbers in the decimal system was overcome by the Hindu-Arabic numeral system. The Hindu-Arabic numeral system assigns positions to the digits of a number, and this method uses base 10 powers; Digits are raised to the nth power according to their position.

For example, take the number 2345.67 in decimal:

The digit 5 ​​takes the place of the ones (10 0 , which is equal to 1),

, which corresponds to 1), 4 stands for the tens (10 1 )

) 3 is in the hundreds place (10 2 )

) 2 is in thousands (10 3 )

) Meanwhile, after the decimal point, the digit 6 is in the tenths place (1/10, that’s 10 -1 ) and the 7 is in the hundredths place (1/100, that’s 10 -2 ).

) and 7 is in the hundredths place (1/100, i.e. 10 ) Thus the number 2345.67 can also be represented as follows: (2 * 103) + (3 * 102) + (4 * 101) + (5 * 100 ) + (6 * 10-1) + (7 * 10-2)

Examples of hex to decimal conversion

(1D9)16 = (473)10

= (473)(80E1)16 = (32993)10

= (32993) (10CE) 16 = (4302) 10

Hexadecimal to Decimal Conversion Table

Hexadecimal Decimal 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 A 10 B 11 C 12 D 13 E 14 F 15 10 16 11 17 12 18 13 19 14 20 15 21 16 22 17 23 18 24 19 25 1a 26 1C 28 1D 29 1F 31 20 33 22 34 23 35 37 27 39 29 41 2a 42 2b 43 2c 45 2E 46 2F 47 48 31 49 49 32 50 33 51 34 52 35 53 36 54 37 55 38 56 39 57 3A 58 3B 59 3C 60 3D 61 3E 62 3F 63 40 64

Hexadecimal Decimal 41 66 43 67 45 69 46 70 48 72 4A 74 4B 76 4D 78 4F 79 50 80 52 54 84 55 56 87 58 88 59 89 5a 90 5b 92 5D 94 5F 95 61 62 99 64 100 66 102 68 104 69 106 6b 107 6c 109 6e 110 6f 111 70 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 115 72 114 73 115 74 116 75 117 76 118 77 119 78 120 79 121 7A 122 7B 123 7C 124 7D 125 7E 126 7F 127 80 128

Hexadepimale decimal number 81 129 83 131 84 133 86 135 88 137 8A 138 8B 139 8C 141 8E 143 90 145 93 94 148 95 149 99 153 9a 154 9b 155 9C 157 9E 158 9F 159 A0 160 A1 162 A3 164 A5 165 A6 167 A8 168 A9 169 AA 170 AC 173 AE 175 B2 178 B3 179 B4 180 B5 181 B6 182 B7 183 B8 184 B9 185 BA 186 BB 187 BC 188 BD 189 BE 190 BF 191 C0 192

How to convert decimal to hexadecimal?

The decimal system is the most well-known number system for the general public. It is base 10 which has only 10 symbols – 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. While the hexadecimal system is the most familiar color representation of the number system in computers or digital systems. It is base 16 which has only 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F. These A, B, C , D , E, F as a single digit instead of double digits 10, 11, 12, 13, 14 and 15 respectively.

Conversion from decimal to hexadecimal number system

There are several direct or indirect methods to convert a decimal number to hexadecimal. An indirect method requires you to convert a decimal number to another number system (e.g. binary or octal), then you can convert it to hexadecimal using the grouping from the binary number system and convert each octal digit to binary and those then group and convert to hexadecimal.

Example − Convert the decimal number 105 to a hexadecimal number.

First convert it to a binary or octal number, = (100) 10 = (1×26+1×25+0x24+0x23+1×22+0x21+0x20) 10 or (1×82+4×81+4×80) 10 because the base of binary and octal is 2 and 8 are respectively. = (1100100) 2 or (144) 8 Then convert each digit of the octal number to a 3-bit binary number and then use the grouping of 4-bit binary number. = (1100100) 2 or (001 100 100) 2 = (110 0100) 2 = (0110 0100) 2 = (6 4) 16 = (64) 16

However, there are two direct methods available for converting a decimal number to hexadecimal: converting with remainders and converting with division. These are explained below.

(a) Converting with remainders (for integer part)

This is a simple method that involves dividing the number to be converted. Let the decimal number be N, then divide that number by 16 because the base of the hexadecimal number system is 16. Write down the value of the remainder, which will be: 0 to 15 (replace 10, 11, 12, 13, 14, 15 with A, B, C, D, E, F). Divide the remaining decimal again until it becomes 0, noting each remainder of each step. Then write the remainders from bottom to top (or in reverse order), which is the hexadecimal equivalent of the given decimal. This is a method of converting an integer to decimal, the algorithm is given below.

Take the decimal as the dividend.

Divide that number by 16 (16 is the base of hexadecimal, so divisor here).

Store the remainder in an array (it will be: 0 to 15 because of divider 16, replace 10, 11, 12, 13, 14, 15 with A, B, C, D, E, F respectively).

Repeat the above two steps until the number is greater than zero.

Print the array in reverse order (which is the equivalent hex of the given decimal).

Note that the dividend (decimal given here) is the number to be divided, the divisor (the base of hexadecimal here, i.e. 16) in the number by which the dividend is divided, and the quotient (remaining divided decimal) the result of is division.

Example − Convert the decimal number 540 to a hexadecimal number.

Since the given number is a decimal integer, use the above algorithm to perform a short divide by 16 with remainder.

Remainder (R) 540 / 16 = 33 12 = C 33 / 16 = 2 1 2 / 16 = 0 2 0 / 16 = 0 0

Now write the rest from the bottom up (in reverse order), this is 021C (or just 21C), which is the hexadecimal number of the decimal integer 540.

However, the above method cannot convert a fraction of a mixed hexadecimal number (a number with integer and fraction). For the decimal fraction, the procedure is explained as follows.

(b) Converting with remainders (for fractions)

Let the decimal fraction be M, then multiply that number by 16 because the base of the hexadecimal number system is 16. Note the value of the integer part, which will be − 0 through 15 (replace 10, 11, 12, 13, 14, 15 with A, B, C, D, E, F). Again, multiply the remaining fractional decimal number until it became 0, noting each integer part of the result of each step. Then write the notated results of the integer part, which is the fractional equivalent of the hexadecimal of the given decimal. This is a method of converting a fractional decimal number, the algorithm is given below.

Take the decimal as the multiplicand.

Multiply this number by 16 (16 is the base of hexadecimal numbers, so multiplier here).

Store the value of the integer part of the result in an array (it will be: 0 to 15, because of multiplier 16, replace 10, 11, 12, 13, 14, 15 with A, B, C, D, E, respectively, F ).

Repeat the above two steps until the number becomes zero.

Print the array (which is the equivalent hexadecimal fraction of the specified decimal fraction).

Note that a multiplicand (here a decimal fraction) is meant to be multiplied by the multiplier (here the base of hexadecimal, i.e. 16).

Example − Convert the fractional decimal number 0.06640625 to a hexadecimal number.

Since the given number is a fractional decimal, using the algorithm above, do a short multiplication by 16 with an integer part.

Multiplication Resulting integer part 0.06640625 x 16 = 1.0625 1 0.0625 x 16 = 1.0 1 0 x 16 = 0.0 0

Now write this resulting integer part. This is approximately 0.110, which is a hexadecimal fraction of 0.06640625.

Convert with division

This method guesses the hexadecimal number of a decimal number. You need to draw a power table of 16. For the integer part, the algorithm is explained as follows.

Start with any decimal number.

Name the powers of 16.

Divide the decimal by the largest power of 16.

Find the rest.

Divide the remainder by the next power of 16.

Repeat until you find the full answer.

Example − Convert the decimal number 380 to a hexadecimal number.

According to above algorithm, power table of 16,

Decimal 163=4096 162=256 161=16 160=1 Hexadecimal number 0 1 7 C

Divide the decimal number by the highest power of 16. = 380 / 256 = 1.484375 So 1 is the first digit or most significant bit (MSB) of the hexadecimal number. Now the remainder = 380 – 1256 = 124 Now divide this remainder by the next power of 16. = 124 / 16 = 7.75 So 7 is the next digit or second highest bit (MSB) of the hexadecimal number. Now the remainder = 124 – 716 = 12 Since the remainder 12 (= C) is less than the base 16, C (= 12) is the smallest (least significant) bit of the required hexadecimal number. Therefore, 17C is the hexadecimal equivalent of the given decimal number 380.

One of the main disadvantages of using binary digits to represent a base 10 decimal number is that the equivalent binary string of ones and zeros can be quite long and confusing.

When working with large digital systems, it is common to find binary numbers made up of 8, 16 and even 32 single digits, making it difficult to both read and write error-free, especially when dealing with many 16- or 32- bit binary numbers is worked .

A common method of overcoming this problem is to arrange the binary numbers in groups or groups of four bits (4 bits). These 4-bit groups use a different type of numbering system, also commonly used in computer and digital systems, called hexadecimal numbers.

Hexadecimal number string

The “Hexadecimal” or just “Hex” number system uses the base-of-16 system and is a popular choice for representing long binary values ​​because its format is quite compact and much simpler compared to long binary strings of ones and zeros is to be understood.

Therefore, as a base-16 system, the hexadecimal number system uses 16 (sixteen) distinct digits with a combination of numbers from 0 to 15. In other words, there are 16 possible digit symbols.

However, there is a potential problem with using this method of digit notation, caused by the fact that the decimal numbers of 10, 11, 12, 13, 14, and 15 are usually written with two adjacent symbols. For example, when we write 10 in hexadecimal, we mean the decimal number ten or the binary number two (1 + 0).

To get around this tricky problem, hexadecimal numbers are used, which have the values ​​of ten, eleven, . . . , fifteen are replaced by the capital letters A, B, C, D, E, and F, respectively.

Then, in the hexadecimal number system, we use the numbers 0 through 9 and capital letters A through F to represent the equivalent of the binary or decimal number, starting with the least significant digit on the right.

As we just said, binary strings can be quite long and difficult to read, but we can make life easier by breaking these large binary numbers into even groups so they’re much easier to write down and understand.

For example, the following group of binary digits 1101 0101 1100 1111 2 is generally much easier to read and understand than 1101010111001111 2 when all binary numbers are combined.

In everyday use of the decimal number system, we use groups of three digits or 000’s from the right to make a very large number like a million or a trillion easier for us to understand, and the same is true in digital systems as well.

Hexadecimal numbers are a more complex system than just using binary or decimal, and are primarily used when dealing with computers and memory addresses. By breaking a binary number into groups of 4 bits, each group or group of 4 digits can now have a possible value between “0000” (0) and “1111” (8+4+2+1 = 15), making a total of 16 different combinations of numbers from 0 to 15. Don’t forget that “0” is also a valid digit.

We remember from our first tutorial on binary numbers that a 4-bit group of digits is called a “nibble”. Since 4 bits are also required to generate a hexadecimal number, a hexadecimal number can also be thought of as a nibble or half byte. Thus, two hexadecimal numbers are required to produce a full byte in the range 00 through FF.

Also, since 16 is the fourth power of 2 (or 24) in the decimal system, there is a direct relationship between the numbers 2 and 16, so a hexadecimal digit has a value equal to four binary digits, so q is now equal to “16”.

Because of this relationship, four digits of a binary number can be represented with a single hexadecimal digit. This makes conversion between binary and hexadecimal very easy, and hexadecimal can be used to write large binary numbers with far fewer digits.

The numbers 0 through 9 are still used as in the original decimal system, but the numbers 10 through 15 are now represented by capital letters of the alphabet from A through F inclusive, and the relationship between decimal, binary, and hexadecimal is given below.

hexadecimal numbers

Decimal number 4-bit binary number Hexadecimal number 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 1011 B 11 1011 B 11 1011 B 12 1 C 12 10 D 14 1110 E 15 1111 F 16 0001 0000 10 (1+0) 17 0001 0001 11 (1+1) Continue up in groups of four

Using the original binary number from above 1101 0101 1100 1111 2, this can now be converted to an equivalent hexadecimal number of D5CF, which is much easier to read and understand than a long string of ones and zeros that we had before.

So by breaking a long length of binary digits into groups of four, starting right to left, we can convert them to hexadecimal notation and represent the same digital number with fewer digits and with a much lower chance of error. Similarly, converting hexadecimal-based numbers back to binary numbers is simply the reverse operation.

Then the main feature of a hexadecimal number system is that there are 16 distinct counting digits from 0 to F, each digit having a weight or value of 16, starting with the least significant bit (LSB).

To distinguish hexadecimal numbers from denary numbers, the actual value of the hexadecimal number, #D5CF or $D5CF, is preceded by either a “#” (hash) or a “$” (dollar sign).

Since the base of a hexadecimal system is 16, which also represents the number of each symbol used in the system, the subscript 16 is used to identify a number expressed in hexadecimal. For example, the previous hexadecimal number is expressed as: D5CF 16

Counting with hexadecimal numbers

So now we know how to convert 4 binary digits to a hexadecimal number. But what if we had more than 4 binary digits, how would we count in hexadecimal beyond the last letter F? The simple answer is to start again with a different set of 4 bits like this.

0…to…9, A,B,C,D,E,F, 10…to…19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21….etc

Don’t get confused, 10 or 20 do NOT represent decimal ten or twenty, they represent 1+0 and 2+0 in hexadecimal notation. In fact, twenty doesn’t even exist as a hexadecimal number. With two hexadecimal digits, we can count up to FF 16, which is 255 10 in decimal.

Likewise, to count higher than FF 16, we would need to add a third hexadecimal digit to the left. Thus, the first 3-bit hexadecimal number would represent 100 16 (256 10 ) and the last would represent FFF 16 (4095 10 ). The maximum 4-digit hexadecimal number is FFFF 16, which equals 65,535 decimal, and so on as the number of digits increases.

Representation of a hexadecimal number

MSB hexadecimal number LSB 168 167 166 165 164 163 162 161 160 4.3G 2.6G 16M 1M 65k 4k 256 16 1st

This addition of additional hexadecimal digits to convert decimal and binary to one hexadecimal is very easy when there are 4, 8, 12 or 16 binary digits to convert. But we can also add zeros to the left of the most significant bit, the MSB, if the number of binary bits is not a multiple of four.

For example, 11001011011001 2 is a 14-bit binary number that is too large for only three hexadecimal digits but too small for a four-digit hexadecimal number. The answer is to add extra zeros to the leftmost bit until we have a complete set of four bit binary numbers or multiples thereof.

Adding extra zeros to a binary number

Binary number 00 11 0010 1101 1001 hexadecimal number 3 2 D 9

This “adding” of zeros applies to any binary number length to find the equivalent hexadecimal number. So, for example, if you had a 9-bit binary number and needed a 4-digit hexadecimal (16-bit) number, 7 zeros would be added to the left of the 9-bit binary number. Enter: 0000000111111111 2 = 01FF 16 and so on.

The main advantage of a hexadecimal number is that it is very compact and the use of a base of 16 means that the number of digits used to represent a given number is usually fewer than binary or decimal numbers. Also, it’s quick and easy to convert between hexadecimal and binary numbers.

Hexadecimal Numbers Example #1

Convert the following binary number 1110 1010 2 to its hexadecimal equivalent.

Binary number = 11101010 2 Group the bits into groups of four starting on the right side = 1110 1010 Find the decimal equivalent of each individual group = 14 10 (in decimal) Using the table above convert them to hexadecimal = E A (in hex) Then , The hexadecimal equivalent of the binary number 1110 1010 2 is #EA 16

Hexadecimal Numbers Example #2

Convert the following hexadecimal number #3FA7 16 to its binary equivalent and also to its decimal or denary equivalent, using subscripts to identify each number system.

#3FA7 16 = 0011 1111 1010 0111 2 = (8192 + 4096 + 2048 + 1024 + 512 + 256 + 128 + 32 + 4 + 2 + 1) = 16,295 10

Then the decimal number 16,295 can be represented as:-

#3FA7 16 in hexadecimal

or

0011 1111 1010 0111 2 in binary.

Summary of hexadecimal numbers

Then to the summary. The hexadecimal or hex number system is widely used in computer and digital systems to reduce large sequences of binary numbers to four digit numbers so that we can easily understand them. The word “hexadecimal” means sixteen because this type of digital numbering system uses 16 different digits from 0 to 9 and A to F.

Hexadecimal numbers group binary numbers into groups of four digits. To convert a binary sequence to an equivalent hexadecimal number, we must first group the binary digits into a set of 4 bits. These binary sets can have any value from 0 10 ( 0000 2 ) to 15 10 ( 1111 2 ), which is the hexadecimal equivalent of 0 to F.

In the next tutorial on binary logic, we will look at converting entire strings of binary numbers to another digital number system called octal numbers and vice versa.

How to fix the problem reported with error code 0x00000001

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A malfunction reported with error code “0x00000001” can occur due to a number of different factors. Common causes are misconfigured system settings or erratic entries in the system items, just to name a few. Such problems can be fixed with special software that repairs system elements and adjusts system settings to restore stability.

The article provides details about the meaning of the problem, possible causes, and possible solutions.

Meaning of error code “0x00000001”

The error code “0x00000001” is an issue name that contains details of the malfunction including why it occurred, what system component or application was at fault, along with some other information. The numeric code in the problem name usually contains data that can be deciphered by the manufacturer of the faulty component or application. The problem with this code can appear in different places within the system so even though it has some detail in its name for a user it is still difficult for a user to locate and fix the cause of the problem without specific technical knowledge or proper software.

Causes for error code “0x00000001”

If you have received this alert on your PC, it means that there has been some glitch in your system operation. Error code 0x00000001 is one of the problems that users can get due to incorrect or failed installation or uninstallation of software that might have left invalid entries in system items. Other possible causes can be an improper system shutdown, e.g. B. due to a power outage, someone with little technical knowledge accidentally deleting a required system file or system item entry, as well as a number of other factors.

Ways to Repair Error Code “0x00000001”

Advanced PC users might be able to fix the issue with this code by manually editing system items, while other users might want to hire a technician to do it for them. However, since any tampering with Windows system items carries the risk of rendering the operating system unbootable, if a user has any doubts about their technical skills or knowledge, they should use a special type of software designed to steal Windows system items without repairing which require special skills of the user.

The following steps should help resolve the issue:

Download the Outbyte PC Repair application

Install and launch the application

Click the Scan Now button to identify possible causes of the problem

Click the Repair All button to fix detected anomalies

The same application can be used to carry out preventive measures to reduce the chances of encountering this or other system problems in the future.

Decimal, Binary, Hex

Decimal versus Binary

When we refer to a number like 532 base 10, we actually mean the number:

(5 * 10^2) + (3 * 10^1) + (2 * 10^0) = 532

Note that in each pair of brackets, the first number of the product is a single-digit number in the range [0, 9], and the second number is a unique power of 10 (in sorted order, largest to smallest).

We can do a similar calculation for numbers in other bases like binary. For example, 0100 in binary (base 2) is equivalent to:

(0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = 0 + 4 + 0 + 0 = 4 (decimal)

Since we are now working with base 2 instead of base 10, all exponent bases are 2’s instead of 10’s, and all first numbers in each bracketed product are integers in the range [0, 1].

However, a number like 0100 could be interpreted as a decimal hundred. So we sometimes prefix binary numbers with “0b” (zero b) to distinguish binary numbers from base 10 numbers (so instead of 0100 we would say that 4 in decimal is equivalent to 0b0100 in binary).

Now let’s try a more complicated example: convert 0b10101001 to a decimal. We assume this is unsigned for now (more on the representation of positive versus negative numbers later).

Number system conversions

When writing programs for microcontrollers we are usually confronted with 3 different number systems: decimal, binary and hexadecimal (or hex). We use the decimal because it is quite natural; that’s how we count. Unfortunately, computers don’t count that way. Because computers and microcontrollers are limited to ones and zeros, they count using sequences of those numbers. This is the binary number system. Binary numbers are usually preceded by the “0b” characters, which are not part of the number. Sometimes they are also divided into groups of 4 to make them easier to read and to better assign them to the hexadecimal number system. An example of a binary number is 0b0100.1011. The dots in the number do not represent anything, they just make the number easier to read.

The binary system is easy to understand, but it takes a lot of digits to use the binary system to represent large numbers. The hexadecimal system can represent much larger numbers with fewer characters and is very similar to binary numbers. Hexadecimal numbers are usually preceded by “0x” characters, which are not part of the number. A single hexadecimal digit can represent four binary digits!

Binary numbers can only consist of ones and zeros; Usually a binary number consists of 8 digits (or a multiple of 8) when used in some kind of computer (or microcontroller). Knowing how to convert a binary number to a decimal number and vice versa is helpful. So how do we convert between number systems? First, consider how we determine the value of a decimal number. The number 268 can be divided into 200 + 60 + 8 or 2 * (10^2) + 6 * (10^1) + 8 * (10^0). There are two important numbers that we need to know in order to “deconstruct” the number – the base of the number system and the position of the digit within the number. The base of a decimal is 10. If we convert the number 268, 2 is the second digit, 6 is the first digit, and 8 is the zero digit. Each digit must be scaled according to its position within the number. The scale of the digit is the base of the number system, raised to the power of the digit’s position in the number. So each number is scaled and then all the scaled digits are added together to find the total value of the number.

The same method can be used to find the value of a binary number. For example, let’s look at the number 0b1011.0101. The base of the binary system is 2 (the 0b prefix is ​​often used in code to indicate that the number is in binary format). The value of our number is: 1*(2^7)+0*(2^6)+1*(2^5)+1*(2^4)+0*(2^3)+1*( 2 ^2)+0*(2^1)+1*(2^0), which equals 181.

0b1011.0101. What a totally inefficient way to enter a number! But we can represent the same binary number with only 2 hexadecimal digits. But first, let’s start by converting a hexadecimal (hex) number to a decimal number, just like we did for a binary number. How about 0xB5? Wait what?! The 0x prefix is ​​used in the code to indicate that the number is written in hex. But what is “B” doing in there? The hexadecimal format is base 16, which means each digit can represent up to 16 different values. Unfortunately, after “9” we run out of digits, so we use letters. The letter “A” stands for 10, “B” for 11, “C” for 12, “D” for 13, “E” for 14 and “F” for 15. “F” is the largest digit in the hexadecimal system. We convert the number in the same way as before. The value of 0xB5 is then: B*(16^1)+5*(16^0) or 181.

Knowing how to convert binary and hex to decimal is important, but probably the most useful number conversion is between hex and binary. These two numbering systems actually work pretty well together. The numbering systems happen to be related in such a way that a single hexadecimal digit represents exactly 4 binary digits, and so 2 hexadecimal digits can represent 8 bits (or binary digits). Here is a table showing how each hexadecimal digit is related to the binary system:

Binary Value Hex Value 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F

For example, to convert the hexadecimal number 0x1C to a binary number, we would find the corresponding binary value for 1 and C and combine them. So 0x1C is binary 0b0001.1100. If we wanted to find out the hex value for a binary number, let’s just go the other way. To find the hex representation of the binary number 0b0010.1011, we first find the hex value for 0010, then the hex value for 1011 and combine them; the hex value would be 0x2B.

There are many free tools to help you convert between these numbering systems, just google “hex number converter”. If you use Windows as operating system, you have a great tool built into the calculator. Just switch the calculator to scientific mode and you can convert between number systems by typing a number and then changing the calculator’s format!

Convert hexadecimal to binary

Hexadecimal to binary conversion is a conversion of a number in a hexadecimal numbering system to a corresponding number in the binary numbering system. The binary number system is a widely used number system. Its main application is in computers. Computers can only understand binary language. All other number systems specified by the user are stored in computers in binary form. So the conversion from hexadecimal to binary is very important.

Here it is not possible to convert it directly, we will convert hexadecimal to decimal, then this decimal number will be converted to binary. Before we get into conversion, let’s discuss binary and hexadecimal numbers.

Binary Numbers: The number that uses only digits 0 and 1, and data in this system is the combination of 0 and 1. It uses only 2 digits, so it is called binary numbers. It is denoted by b 2, where b is any binary number.

Examples: 1) 010111 2 2 ) 00111011 2 3) 111 2

Hexadecimal Number: Hexa means 16. The hexadecimal system uses 16 digits. It consists of numbers and letters. It contains the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F; 16 digits in total. It is denoted by s 16, where s is a hexadecimal number.

Examples: 1) A1 16 2) EE9 16 3) FD654 16

Also read:

Hex to binary table

Here is the table for hex to binary conversion. The table is given for the first digits up to 16.

Hexadecimal number Binary number 0 0 1 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001 A 1010 B 1011 C 1100 D 1101 E 1110 F 1111

How do I convert hexadecimal numbers to binary numbers?

To convert a hexadecimal number to its equivalent binary number, follow the steps given here:

Step 1: Take the given hexadecimal number

Take the given hexadecimal number Step 2: Find the number of digits in the decimal number

Find the number of decimal places Step 3: If it has n digits, multiply each digit by 16 n-1, where the digit is in the nth place

If it has n digits, multiply each digit by 16, taking the digit in the nth place. Step 4: Add the terms after multiplication

Add the terms after the multiplication Step 5: The result is the decimal number that corresponds to the given hexadecimal number. Now we need to convert this decimal number to a binary number.

The result is the decimal number that corresponds to the given hexadecimal number. Now we need to convert this decimal number to a binary number. Step 6: Divide the decimal number by 2

Divide the decimal by 2. Step 7: Write down the rest

Record the remainder Step 8: Do the above 2 steps for the quotient until the quotient is zero

Do the above 2 steps for the quotient until the quotient is zero. Step 9: Write the remainders in reverse order.

Write the remainders in reverse order. Step 10: The result is the desired binary number.

Therefore, from the above steps, it is clear that we can convert any hexadecimal number to binary number, i.e. first we need to convert a hexadecimal number to a decimal number and then a decimal number to a binary number.

Hexa to binary examples

Question 1: Convert A2B 16 to an equivalent binary number.

Solution: Given hexadecimal number = A2B 16

First convert the given hexadecimal number to the corresponding decimal number.

A2B 16 = (A × 162) + (2 × 161) + (B × 160)

= (A × 256) + (2 × 16) + (B × 1)

= (10 × 256) + 32 + 11

= 2560 + 43

= 2603 (decimal number)

Now we need to convert 2603 10 to binary

The binary number obtained is 101000101011 2

Therefore A2B 16 = 101000101011 2

Exercise 2: Convert E 16 into an equivalent binary number.

Solution: Given is a hexadecimal number E.

First convert the given hexadecimal number to the corresponding decimal number.

E16 = E×160

= E × 1

= E

=14 (decimal number)

Now we need to convert 14 10 to a binary number.

The binary number obtained is 1110 2

Therefore E 16 = 1110 2

Task 3: Convert 30 16 to an equivalent binary number.

Solution: Suppose the hexadecimal number is 30

First convert the given hexadecimal number to the corresponding decimal number.

30 16 = (3 × 161) + (0 × 160)

= 48 + 0

= 48 (decimal number)

Now we need to convert 48 10 to binary.

Because of this,

The binary number is 110000 2

So 30 16 = 110000 2

exercise problems

number systems

Decimal number system (base 10)

Uses 10 digits: 0 – 9

125 = 1*102 + 2*101 + 5*100

Binary Number System (Base 2)

Uses 2 digits: 0 and 1

110101 = 1*25 + 1*24 + 0*23 + 1*22 + 0*21 + 1*20

Hexadecimal number system (base 16)

Uses 16 symbols: 0-9, A, B, C, D, E, F

19F = 1*162 + 9*161 + 15*160

Decimal binary hexadenzi -time 0 1 0001 1 2 0011 3 4 0100 4 5 6 0110 6 7 8 1000 8 9 1001 1010 A 11 1011 B 12 1100 C 13110 E 15 1111 f

Convert Binary => Hexadecimal

Starting from the right, divide the zeros and ones into groups of four. Pad with zeros on the left as needed to form a group of four. Find the corresponding hexadecimal value from the table.

11011011100011 = 0011 0110 1110 0011 = 3 6E 3 = 36E3

Convert Hexadecimal => Binary

Convert each symbol to its corresponding binary value.

2AF = 2AF = 0010 1010 1111 = 001010101111

Convert Binary/Hexadecimal => Decimal

Multiply each symbol by the base value, which is elevated to a positional power, then add each product.

11011 = 1*2 4 + 1*2 3 + 0*2 2 + 1*2 1 + 1*2 0 = 27

2AF = 2*162 + 10*161 + 15*160 = 687

Convert Decimal => Binary/Hexadecimal

Divide by the base value until the quotient is 0. When you convert to hex, you convert the remainders to hex.

415 (decimal) = 19F (hex) 0 16 Ö 1 R1 => 1 16 Ö 25 R9 => 9 16 Ö 415 R15 => F

arithmetic

Binary addition

1 11 0 0 1 1 1 + 0 + 1 + 0 + 1 + 1 0 1 1 10 11 111111 11010110 + 1101101 101000011

Binary Subtraction

02 0 1 1 10 – 0 – 0 – 1 – 1 0 1 0 1 1 0 2 202 02 1 10010 11 10 – 11010001 1001011101

Hexadecimal addition

A27CB4 39CDF106 + 6E3095 + A6F278C 110AD49 443D1892

Hexadecimal subtraction

A52CF3 3B0029 – 2B7169 – 1765A4 79BB8A 239A85

storage

The main memory of a computer memory consists of bits (also called binary digits).

1 bit => binary 0 or 1 1 byte => 8 bits => 2 hex digits 1 half word => 2 bytes => 16 bits => 4 hex digits 1 full word => 4 bytes => 32 bits => 8 hex -digits => 2 half words 1 double word => 8 bytes => 64 bits => 16 hex digits => 2 whole words

Largest positive hexadecimal value that can be stored: 7 FFFFFFF

If the first digit is 0 – 7, positive hexadecimal number.

If the first digit is 8 – F, negative hexadecimal number.

Largest positive binary value: 0 1111111111111111111111111111111

The first digit is called the sign bit

If 0, positive binary number

If 1, negative.

Negative numbers are stored by taking the two’s complement of the absolute value of the number.

To find the complement of binary 2:

Switch all 0’s to 1’s and 1’s to 0’s (find the 1’s complement) Add 1

100111100 => 011000011 + 1 011000100

To find the hexadecimal 2’s complement:

Subtract the number from FFFFFFFF Add 1

FFFFFFFF FFFFFFFF FFFFFFFF – 002BCF06 – 00000001 – FFD430FA FFD430F9 FFFFFFFE 002BCF05 + 1 + 1 + 1 FFD430FA FFFFFFFF 002BCF06

Calculating with the two’s complement:

Addition – same

Subtraction – Find the two’s complement of subtrahend (# after the subtraction sign) and add it to the number

overflow:

Occurs when a number becomes too large for its representation scheme.

Check for overflow:

Convert the 1st digit of any number to binary. Add the binary values ​​together. If the last two carry bits are the same, no rollover. If they are different, overflow.

Refer to this table for helpful information on converting ASCII, decimal, hexadecimal, octal, and binary values.

Table 1. Conversions between ASCII, decimal, hexadecimal, octal, and binary values ​​ASCII Decimal Hexadecimal Octal Binary zero 0 0 0 0 Start of header 1 1 1 1 Start of text 2 2 2 2 10 End of text 3 3 3 11 End transmission 4 4 4 100 request 5 5 5 101 acknowledgment 6 6 6 110 ring 7 7 7 111 backspace 8 8 10 1000 horizontal tab 9 9 11 1001 line feed 10 A 12 1010 vertical tab 11 B 13 1011 form feed 12 C 14 1100 carriage return 13 D 15 1101 Shift out 14 E 16 1110 Shift in 15 F 17 1111 Data Link Escape 16 10 20 10000 Device Control 1/Xon 17 11 21 10001 Device Control 2 18 12 22 10010 Device Control 3/Xoff 19 13 23 10010 Device Control 10 4 0.240 10011 Device Control 10 4 Negative receipt 21 15 25 10101 Synchronous resting state 22 16 26 10110 Transmission block end 23 17 10111 Demolition 24 18 30 11000 Medium ends 25 19 31 11001 File/ Replacement 26 1a 32 11010 Escape 37 File Racing Signs 28 1c 34 11100 Data Setting Signs 30 1E 36 11110 unit separator 31 1F 37 11111 space 32 20 40 100000 ! 33 21 41 100001 “34 22 42 100010 # 35 23 100011 $ 36 24 45 45 100101 & 38 26 46 100110 ’39 47 100111 (40 28 50 101000) 41 29 51 101001 * 42 2a 52 101010 + +1010 +101000) 43 2B 53 101011, 44 2C 54 101100 – 45 2D 55 101101. 52 34 64 110100 53 35 65 110101 6 66 110110 7 55 37 38 70 111000 9 57 39 71 1110010; 59 3B 73 111100 = 61 3D 75 1111111> 62 3E 76 11111111111? 63 3F 77 111111 @ 64 40 1000000 a 65 41 1000001 B 66 42 1000011 D 68 44 104 10001001 F 70 46 1000110 G 71 47 1000111 72 48 110 1001000 I. 73 49 111 1001001 J 74 1001010 K 75 4B 113 4C 114 1001100 M 77 4D 115 1001110 O 79 4F 117 1001111 P 80 120 1010000 Q 81 1010001 83 53 123 1010011 T 84 54 124 1010100 U 85 55 125 1010101 V 86 56 1 26 1010110 W 87 127 1010111 x 88 130 1011000 Y 89 131 1011001 Z 90 5A 132 1011010 [91 5B 133 1011011 \ 92 5C 134 1011100] 93 5D 135 5e 136 1011110 _ 95 5F 137 101111 `96 60 140 1100000 A 97 61 1100001 B 98 62 1100010 C 99 63 1100011 D 100 64 1100100 E 101 65 1100101 F 102 66 1100110 G 103 67 1100111 H 104 68 150 1101000 K 107 6B 153 1101011 L 108 6c 154 1101100 M 109 6d 155 110 6e 156 1101110 O 11101111 P 112 70 160 113 71 1611001 R 114 72 162 115 73 163100100100101001001 R 114 72 162 111001010010 S 115 731001001 R 116 262 111001010010 S 115 73 1631001 R. 74 1110100 U 117 75 1110101 V 118 77 167 1110111 x 120 78 171 79 171 1111001 Z 122 7A 1111010 {123 7b 173 1111011 | 124 7C 174 111100} 125 75 1111101 ~ 126 7E 177 7F 177 1111111 128 808 10000001 130 82 10000011 132 84 204 10000101 134 86 2000110 135 207 10000111 136 88 210 10001000 137 10001001 138 8a 212 10001011 140 8C 214 10001101 142 8E 216 10001111 144 90 220 1001,00010010010 147 93100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100 94 224 100100 149 95 10010101 150 96 10010110 151 227 10010000 153 99 231 10011001 154 9a 233 10011011 156 9C 234 100100000 162 A2 242 10100010100011 A4 244 10100100 165 A5 245 10100101 166 A6 246 10100110 167 10100111 168 A8 250 10101000 169 A9 251 10101001 170 AA 252 10101011 172 AC 254 1010100 173 255 n. 10101111 176 B0 260 10110000 1 77 B1 261 10110001 178 B2 262 10110010 179 B3 263 10110011 180 B4 264 10110101 182 B6 266 10110110 183 B8 270 1011000 185 B9 272 101111011 188 BB 272 101111111111111111111111111111111111111111 188 275 1011101 190 BE 276 1011110 191 BF 277 1011111 192 C0 300 11000000 194 11000001 194 C2 110000101010101111111111110 199 C7 307 11001000 201 CAC 11001100 205 CD 315 11001101 206 CE 316 1100110 207 D3 323 11010011 212 D4 324 11010100 213 D5 325 11010101 214 D6 326 11010110 215 D7 327 11010111 216 D8 330 11011000 217 D9 331 11011001 218 DA 332 11011010 219 DB 333 11011011 220 DC 334 11011100 221 DD 335 11011101 222 DE 336 11011110 223 DF 337 111 224 E0 341 11100001 226 E2 342 11100010 227 E4 344 11100100 229 E6 346 11100110 231 E7 347 11100110 231 E7 347 111001110 231 E7 347 1110110 231 E7 347 1110110 231 E7 347 1110110 231 E7 347 1110110 231 E7 347 1110110 231 E7 347 11101110 231 E7 347 11101110 231 E7 347 111011110 231 E7 347 347 347 347. 11101000 233 E9 351 11101001 234 EA 352 11101010 235 EB 353 11101011 236 EC 354 11101100 237 ED 355 11101101 238 EE 356 11101110 239 EF 357 11101111 240 F0 360 11110000 241 F1 361 11110001 242 F2 362 11110010 243 F3 363 11110011 244 F4 364 11110100 245 F5 365 11110101 246 F6 366 11110110 247 11110111 248 F8 370 1111000 241 11111001 250 FA 372 11111011 252 FC 374 11111100 253 FD 375 1111110 371 11.

Hexadecimal number system

The hexadecimal number system is a type of number system that has a base value of 16. It is also sometimes pronounced “Hex”. Hexadecimal numbers are represented by only 16 symbols. These symbols or values ​​are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Each digit represents a decimal value. For example, D equals base-10 13.

Hexadecimal number systems can be converted to other number systems such as binary (base 2), octal (base 8), and decimal (base 10). The concept of the number system is explained in detail in the Year 9 syllabus.

The list of the 16 hexadecimal digits with their equivalent decimal, octal, and binary representation is given here in the form of a table to help with number system conversion. This list can also be used as a translator or converter.

System table for hexadecimal numbers

Below is the table of hexadecimal number systems with equivalent values ​​of binary and decimal number systems.

Decimal numbers 4-bit binary number Hexadecimal number 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 B 1 1 1010 C 011 C 0 11 B 1 D 14 1110 E 15 1111 F

Below is the link to download the spreadsheet. Students can download the PDF and study offline as well.

Conversions from hexadecimal number systems

As we know, in the hexadecimal number system, there are 16 digits that are represented from 0 to 9 like decimal numbers, but after that it starts alphabetical representation of preceding numbers like A, B, C, D and E. Let’s see the conversion of ‘hex’ into other number systems.

Conversion from hexadecimal to decimal

Here you can see the representation of a hexadecimal number in decimal form.

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Decimal to hexadecimal conversion

You have learned to convert hexadecimal numbers to decimal numbers. Now let’s figure out how we can convert a decimal number to a hexadecimal number system. Follow the steps below:

First divide the number by 16

Take the quotient and divide it by 16 again

The remainder gives the hex value

Repeats the steps until the quotient becomes 0

Example: Convert (242) 10 to hexadecimal.

Solution: Divide 242 by 16 and repeat the steps until the quotient stays at 0.

Therefore (242) 10 = (F2) 16

Conversion from hexadecimal to octal

Here you can see the representation of a hexadecimal number in octal number form.

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Octal 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17

Octal to hexadecimal conversion

To convert octal to hex, we first need to convert the octal number to decimal, and then convert decimal to hexadecimal. Let’s understand it with an example;

Example: Convert (121) 8 to hexadecimal.

Solution: First convert 121 to a decimal number.

⇒ 1×82 + 2×81 + 1×80

⇒ 1×64 + 2×8 + 1×1

⇒ 64 + 16 + 1

⇒ 81

(121) 8 = 81 10

Now convert 81 10 to a hexadecimal number.

So 81 10 = 51 16

Conversion from hexadecimal to binary

Here you can see the representation of a hexadecimal number in binary form. We can only use 4 digits to represent each hexadecimal number, each group having a different value of 0000 (for 0) and 1111 (for F=15=8+4+2+1).

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Binary 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111

Binary to hexadecimal conversion

Binary to hexadecimal conversion is a simple method. You just have to set the values ​​of the binary number to the corresponding hexadecimal number.

Example: Convert (11100011) 2 to hexadecimal.

Solution: From the table we can write 11100011 as E3.

Therefore (11100011) 2 = (E3) 16

Facts about the hexadecimal number system

Of many types of number representation techniques, the hexadecimal number system is a base-16 number system.

So hexadecimal numbers have 16 symbols or digital values, so 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

A, B, C, D, E, F are single bit representations of 10, 11, 12, 13, 14, and 15, respectively.

Adding either an o prefix or an h prefix displays hexadecimal.

A power of 16 is the weight of each digit’s position.

Solved examples of the hexadecimal number system

Example 1: What is 5C6 (hexadecimal)?

Solution: Step 1: The “5” is the position “16 x 16”, so 5 x 16 x 16

Step 2: The “C” (12) is in position “16”, i.e. 12 x 16.

Step 3: The “6” in position “1”, i.e. 6.

Answer is: 5C6 = 5 x 16 x 16 + 12 x 16 +6 = (1478 ) in decimal.

Example 2: What is 3C5 (Hexadecimal)?

Solution: Step 1: The “3” is the position “16 x 16”, so 3 x 16 x 16

Step 2: The “C” (12) is in position “16”, i.e. 12 x 16.

Step 3: The “5” is in position “1”, which means 5.

Answer is: 3C5 = 3 x 16 x 16 + 12 x 16 + 5 = (965) in decimal.

Example 3: What is 7B5 (hexadecimal)?

Solution: Step 1: The “7” is the position “16 x 16”, so 7 x 16 x 16

Step 2: The “B” (11) is in position “11”, i.e. 11 x 16.

Step 3: The 5″ in the “1” position, meaning 5.

Answer is: 7B5 = 7 x 16 x 16 + 11 x 16 +5 = (1973) in decimal.

Example 4: What is 2E8 (Hexadecimal)?

Solution: Step 1: The “2” is the position “16 x 16”, so 2 x 16 x 16

Step 2: The “E” (14) is in position “16”, i.e. 14 x 16.

Step 3: The “2” is in the “1” position, which means 2.

Answer is: 2E8 = 2 x 16 x 16 + 14 x 16 +8 = (744) in decimal.

Example 5: What is 4F8 (Hexadecimal)?

Solution: Step 1: The “4” is the “16 x 16” position, so 4 x 16 x 16

Step 2: The “F” (15) is in position “16”, i.e. 15 x 16.

Step 3: The “8” is in the “1” position, which means 8.

Answer is: 4F8 = 4 x 16 x 16 + 15 x 16 + 8 = (1272) in decimal.

practice questions

What is 5D 16 in decimal?

as a decimal number? Convert the decimal number 21 to a hexadecimal number.

What is 0110111 2 in hexadecimal?

Related Articles

Keep visiting BYJU’S and subscribe to our YouTube channel to learn number systems and other math topics in a fun and engaging way.

Hexadecimal number system

The hexadecimal number system is a type of number system that has a base value of 16. It is also sometimes pronounced “Hex”. Hexadecimal numbers are represented by only 16 symbols. These symbols or values ​​are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Each digit represents a decimal value. For example, D equals base-10 13.

Hexadecimal number systems can be converted to other number systems such as binary (base 2), octal (base 8), and decimal (base 10). The concept of the number system is explained in detail in the Year 9 syllabus.

The list of the 16 hexadecimal digits with their equivalent decimal, octal, and binary representation is given here in the form of a table to help with number system conversion. This list can also be used as a translator or converter.

System table for hexadecimal numbers

Below is the table of hexadecimal number systems with equivalent values ​​of binary and decimal number systems.

Decimal numbers 4-bit binary number Hexadecimal number 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 B 1 1 1010 C 011 C 0 11 B 1 D 14 1110 E 15 1111 F

Below is the link to download the spreadsheet. Students can download the PDF and study offline as well.

Conversions from hexadecimal number systems

As we know, in the hexadecimal number system, there are 16 digits that are represented from 0 to 9 like decimal numbers, but after that it starts alphabetical representation of preceding numbers like A, B, C, D and E. Let’s see the conversion of ‘hex’ into other number systems.

Conversion from hexadecimal to decimal

Here you can see the representation of a hexadecimal number in decimal form.

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Decimal to hexadecimal conversion

You have learned to convert hexadecimal numbers to decimal numbers. Now let’s figure out how we can convert a decimal number to a hexadecimal number system. Follow the steps below:

First divide the number by 16

Take the quotient and divide it by 16 again

The remainder gives the hex value

Repeats the steps until the quotient becomes 0

Example: Convert (242) 10 to hexadecimal.

Solution: Divide 242 by 16 and repeat the steps until the quotient stays at 0.

Therefore (242) 10 = (F2) 16

Conversion from hexadecimal to octal

Here you can see the representation of a hexadecimal number in octal number form.

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Octal 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17

Octal to hexadecimal conversion

To convert octal to hex, we first need to convert the octal number to decimal, and then convert decimal to hexadecimal. Let’s understand it with an example;

Example: Convert (121) 8 to hexadecimal.

Solution: First convert 121 to a decimal number.

⇒ 1×82 + 2×81 + 1×80

⇒ 1×64 + 2×8 + 1×1

⇒ 64 + 16 + 1

⇒ 81

(121) 8 = 81 10

Now convert 81 10 to a hexadecimal number.

So 81 10 = 51 16

Conversion from hexadecimal to binary

Here you can see the representation of a hexadecimal number in binary form. We can only use 4 digits to represent each hexadecimal number, each group having a different value of 0000 (for 0) and 1111 (for F=15=8+4+2+1).

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Binary 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111

Binary to hexadecimal conversion

Binary to hexadecimal conversion is a simple method. You just have to set the values ​​of the binary number to the corresponding hexadecimal number.

Example: Convert (11100011) 2 to hexadecimal.

Solution: From the table we can write 11100011 as E3.

Therefore (11100011) 2 = (E3) 16

Facts about the hexadecimal number system

Of many types of number representation techniques, the hexadecimal number system is a base-16 number system.

So hexadecimal numbers have 16 symbols or digital values, so 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

A, B, C, D, E, F are single bit representations of 10, 11, 12, 13, 14, and 15, respectively.

Adding either an o prefix or an h prefix displays hexadecimal.

A power of 16 is the weight of each digit’s position.

Solved examples of the hexadecimal number system

Example 1: What is 5C6 (hexadecimal)?

Solution: Step 1: The “5” is the position “16 x 16”, so 5 x 16 x 16

Step 2: The “C” (12) is in position “16”, i.e. 12 x 16.

Step 3: The “6” in position “1”, i.e. 6.

Answer is: 5C6 = 5 x 16 x 16 + 12 x 16 +6 = (1478 ) in decimal.

Example 2: What is 3C5 (Hexadecimal)?

Solution: Step 1: The “3” is the position “16 x 16”, so 3 x 16 x 16

Step 2: The “C” (12) is in position “16”, i.e. 12 x 16.

Step 3: The “5” is in position “1”, which means 5.

Answer is: 3C5 = 3 x 16 x 16 + 12 x 16 + 5 = (965) in decimal.

Example 3: What is 7B5 (hexadecimal)?

Solution: Step 1: The “7” is the position “16 x 16”, so 7 x 16 x 16

Step 2: The “B” (11) is in position “11”, i.e. 11 x 16.

Step 3: The 5″ in the “1” position, meaning 5.

Answer is: 7B5 = 7 x 16 x 16 + 11 x 16 +5 = (1973) in decimal.

Example 4: What is 2E8 (Hexadecimal)?

Solution: Step 1: The “2” is the position “16 x 16”, so 2 x 16 x 16

Step 2: The “E” (14) is in position “16”, i.e. 14 x 16.

Step 3: The “2” is in the “1” position, which means 2.

Answer is: 2E8 = 2 x 16 x 16 + 14 x 16 +8 = (744) in decimal.

Example 5: What is 4F8 (Hexadecimal)?

Solution: Step 1: The “4” is the “16 x 16” position, so 4 x 16 x 16

Step 2: The “F” (15) is in position “16”, i.e. 15 x 16.

Step 3: The “8” is in the “1” position, which means 8.

Answer is: 4F8 = 4 x 16 x 16 + 15 x 16 + 8 = (1272) in decimal.

practice questions

What is 5D 16 in decimal?

as a decimal number? Convert the decimal number 21 to a hexadecimal number.

What is 0110111 2 in hexadecimal?

Related Articles

Keep visiting BYJU’S and subscribe to our YouTube channel to learn number systems and other math topics in a fun and engaging way.

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One of the main disadvantages of using binary digits to represent a base 10 decimal number is that the equivalent binary string of ones and zeros can be quite long and confusing.

When working with large digital systems, it is common to find binary numbers made up of 8, 16 and even 32 single digits, making it difficult to both read and write error-free, especially when dealing with many 16- or 32- bit binary numbers is worked .

A common method of overcoming this problem is to arrange the binary numbers in groups or groups of four bits (4 bits). These 4-bit groups use a different type of numbering system, also commonly used in computer and digital systems, called hexadecimal numbers.

Hexadecimal number string

The “Hexadecimal” or just “Hex” number system uses the base-of-16 system and is a popular choice for representing long binary values ​​because its format is quite compact and much simpler compared to long binary strings of ones and zeros is to be understood.

Therefore, as a base-16 system, the hexadecimal number system uses 16 (sixteen) distinct digits with a combination of numbers from 0 to 15. In other words, there are 16 possible digit symbols.

However, there is a potential problem with using this method of digit notation, caused by the fact that the decimal numbers of 10, 11, 12, 13, 14, and 15 are usually written with two adjacent symbols. For example, when we write 10 in hexadecimal, we mean the decimal number ten or the binary number two (1 + 0).

To get around this tricky problem, hexadecimal numbers are used, which have the values ​​of ten, eleven, . . . , fifteen are replaced by the capital letters A, B, C, D, E, and F, respectively.

Then, in the hexadecimal number system, we use the numbers 0 through 9 and capital letters A through F to represent the equivalent of the binary or decimal number, starting with the least significant digit on the right.

As we just said, binary strings can be quite long and difficult to read, but we can make life easier by breaking these large binary numbers into even groups so they’re much easier to write down and understand.

For example, the following group of binary digits 1101 0101 1100 1111 2 is generally much easier to read and understand than 1101010111001111 2 when all binary numbers are combined.

In everyday use of the decimal number system, we use groups of three digits or 000’s from the right to make a very large number like a million or a trillion easier for us to understand, and the same is true in digital systems as well.

Hexadecimal numbers are a more complex system than just using binary or decimal, and are primarily used when dealing with computers and memory addresses. By breaking a binary number into groups of 4 bits, each group or group of 4 digits can now have a possible value between “0000” (0) and “1111” (8+4+2+1 = 15), making a total of 16 different combinations of numbers from 0 to 15. Don’t forget that “0” is also a valid digit.

We remember from our first tutorial on binary numbers that a 4-bit group of digits is called a “nibble”. Since 4 bits are also required to generate a hexadecimal number, a hexadecimal number can also be thought of as a nibble or half byte. Thus, two hexadecimal numbers are required to produce a full byte in the range 00 through FF.

Also, since 16 is the fourth power of 2 (or 24) in the decimal system, there is a direct relationship between the numbers 2 and 16, so a hexadecimal digit has a value equal to four binary digits, so q is now equal to “16”.

Because of this relationship, four digits of a binary number can be represented with a single hexadecimal digit. This makes conversion between binary and hexadecimal very easy, and hexadecimal can be used to write large binary numbers with far fewer digits.

The numbers 0 through 9 are still used as in the original decimal system, but the numbers 10 through 15 are now represented by capital letters of the alphabet from A through F inclusive, and the relationship between decimal, binary, and hexadecimal is given below.

hexadecimal numbers

Decimal number 4-bit binary number Hexadecimal number 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 1011 B 11 1011 B 11 1011 B 12 1 C 12 10 D 14 1110 E 15 1111 F 16 0001 0000 10 (1+0) 17 0001 0001 11 (1+1) Continue up in groups of four

Using the original binary number from above 1101 0101 1100 1111 2, this can now be converted to an equivalent hexadecimal number of D5CF, which is much easier to read and understand than a long string of ones and zeros that we had before.

So by breaking a long length of binary digits into groups of four, starting right to left, we can convert them to hexadecimal notation and represent the same digital number with fewer digits and with a much lower chance of error. Similarly, converting hexadecimal-based numbers back to binary numbers is simply the reverse operation.

Then the main feature of a hexadecimal number system is that there are 16 distinct counting digits from 0 to F, each digit having a weight or value of 16, starting with the least significant bit (LSB).

To distinguish hexadecimal numbers from denary numbers, the actual value of the hexadecimal number, #D5CF or $D5CF, is preceded by either a “#” (hash) or a “$” (dollar sign).

Since the base of a hexadecimal system is 16, which also represents the number of each symbol used in the system, the subscript 16 is used to identify a number expressed in hexadecimal. For example, the previous hexadecimal number is expressed as: D5CF 16

Counting with hexadecimal numbers

So now we know how to convert 4 binary digits to a hexadecimal number. But what if we had more than 4 binary digits, how would we count in hexadecimal beyond the last letter F? The simple answer is to start again with a different set of 4 bits like this.

0…to…9, A,B,C,D,E,F, 10…to…19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21….etc

Don’t get confused, 10 or 20 do NOT represent decimal ten or twenty, they represent 1+0 and 2+0 in hexadecimal notation. In fact, twenty doesn’t even exist as a hexadecimal number. With two hexadecimal digits, we can count up to FF 16, which is 255 10 in decimal.

Likewise, to count higher than FF 16, we would need to add a third hexadecimal digit to the left. Thus, the first 3-bit hexadecimal number would represent 100 16 (256 10 ) and the last would represent FFF 16 (4095 10 ). The maximum 4-digit hexadecimal number is FFFF 16, which equals 65,535 decimal, and so on as the number of digits increases.

Representation of a hexadecimal number

MSB hexadecimal number LSB 168 167 166 165 164 163 162 161 160 4.3G 2.6G 16M 1M 65k 4k 256 16 1st

This addition of additional hexadecimal digits to convert decimal and binary to one hexadecimal is very easy when there are 4, 8, 12 or 16 binary digits to convert. But we can also add zeros to the left of the most significant bit, the MSB, if the number of binary bits is not a multiple of four.

For example, 11001011011001 2 is a 14-bit binary number that is too large for only three hexadecimal digits but too small for a four-digit hexadecimal number. The answer is to add extra zeros to the leftmost bit until we have a complete set of four bit binary numbers or multiples thereof.

Adding extra zeros to a binary number

Binary number 00 11 0010 1101 1001 hexadecimal number 3 2 D 9

This “adding” of zeros applies to any binary number length to find the equivalent hexadecimal number. So, for example, if you had a 9-bit binary number and needed a 4-digit hexadecimal (16-bit) number, 7 zeros would be added to the left of the 9-bit binary number. Enter: 0000000111111111 2 = 01FF 16 and so on.

The main advantage of a hexadecimal number is that it is very compact and the use of a base of 16 means that the number of digits used to represent a given number is usually fewer than binary or decimal numbers. Also, it’s quick and easy to convert between hexadecimal and binary numbers.

Hexadecimal Numbers Example #1

Convert the following binary number 1110 1010 2 to its hexadecimal equivalent.

Binary number = 11101010 2 Group the bits into groups of four starting on the right side = 1110 1010 Find the decimal equivalent of each individual group = 14 10 (in decimal) Using the table above convert them to hexadecimal = E A (in hex) Then , The hexadecimal equivalent of the binary number 1110 1010 2 is #EA 16

Hexadecimal Numbers Example #2

Convert the following hexadecimal number #3FA7 16 to its binary equivalent and also to its decimal or denary equivalent, using subscripts to identify each number system.

#3FA7 16 = 0011 1111 1010 0111 2 = (8192 + 4096 + 2048 + 1024 + 512 + 256 + 128 + 32 + 4 + 2 + 1) = 16,295 10

Then the decimal number 16,295 can be represented as:-

#3FA7 16 in hexadecimal

or

0011 1111 1010 0111 2 in binary.

Summary of hexadecimal numbers

Then to the summary. The hexadecimal or hex number system is widely used in computer and digital systems to reduce large sequences of binary numbers to four digit numbers so that we can easily understand them. The word “hexadecimal” means sixteen because this type of digital numbering system uses 16 different digits from 0 to 9 and A to F.

Hexadecimal numbers group binary numbers into groups of four digits. To convert a binary sequence to an equivalent hexadecimal number, we must first group the binary digits into a set of 4 bits. These binary sets can have any value from 0 10 ( 0000 2 ) to 15 10 ( 1111 2 ), which is the hexadecimal equivalent of 0 to F.

In the next tutorial on binary logic, we will look at converting entire strings of binary numbers to another digital number system called octal numbers and vice versa.

This is a conversion table of decimal numbers alongside their binary and hexadecimal equivalents. The matching ASCII characters are also listed, with more detailed descriptions of some characters on this page. If none of these words mean anything to you, skip to the bottom of this page for more information:

ASCII codes 0 to 127

No. Binerer Hex ASCII Description 0 00000000 0H NULL 1 00000001 1H Start of the hot 2 00000010 2H Stex of the text 3 00000011 3H End of the text 4 00000100 4H End of the transmission 5 0000010 6H Recognition 7 000001117,000 8H Rack Rack rack rack rack rack rack rack rack rack 00001001 9H horizontal tab 10 00001010 AH Line feed 11 00001011 BH Stical Tab 12 00001100 CH Form feed 13 00001101 DH WATE return 14 00001110 EH switching shifting OUT OUT OUT OUT OUT OUT OUT OUT OURN 15H Negative Recognition 22 00010110 16H 1Ch File Separator 29 00011101 1Dh Group Separator 30 00011110 1Eh Record Separator 31 00011111 1Fh Unit Separator 32 00100000 20h Space 33 00100001 21h ! Exclusion marks Mark 34 00100010 22H “Double quotes 35 00100010 23H # Numbers or Hash -Tag 36 00100100 $ $ $ 37 00100101 25H % percent characters 38 00100110 26H & amperand 39 001001001001 29H ‘1 0010101000 (left rights 42 0010101011 Sternchen 43 00101011 2BH + plus signs 44 00101100 2CH, comma 45 00101101 2DH – binding or minus sign 46 0010110 2EH. Period 47 0010111 2FH / SLASH 48 00110000 30H 1 One 50 00110010 32H 2 TWO 51 0011001 33H 3 Throw Thrinking 5. 53 00110101 35H 54 00110110 36H 6 SIX 55 00110111 37H 7 SEVE 56 0011000 38H 8 Eight 57 0011001 39H 9 Nine 58 00111010 3AH: Down-point 59 00111011 3BH; = equals sign 62 00111110 3Eh > greater than sign 63 00111111 3Fh ? Apital D 69 01000101 45H E 70 01000110 46H F 710001011 47H G Capital G Kapital G. 72 01001000 48H H Capital H 73 01001001 49H I Capital I 74 01001010 4AH J Capital J 75 01001011 4BH K CAP 76 01001100 4CH L Capital L 77 01001101 4DH M Capital M 78 01001010010000 N Capital P 81 01010001 51H Q Capital Q 82 01010010 52H R Capital R 83 0101001 59H y Capital Y 90 01011011101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 [LEFT Bracket 92 0101100 5CH \ Backslash 93 0101101 5DH] Right Bracket 94 0101110 5H ^ Caret Or CircumFllex 95 0101111 5FH _ Underscore 96 0100000 60H `GRAVE Accent 97 01100001 CHECH A 98 0100010 62H B. 100 01100100 64H D Small letters D 101 01100101 65H E small letter E 102 01100110 66H F Small letters F 103 01100111 67H G Small letters G 104 01101000 68H H Aboin 10101101001 69H Small letters J 107 0110101011 6BH K KleinbuC hletter K 108 01101100 6ch L lowercase L 109 01101101 6dh M lowercase M 110 01101110 6eH 115 01110011 73H 7Bh { left bracket 124 01111100 7Ch | bar 125 01111101 7Dh } right bracket 126 01111110 7Eh ~ tilde or equivalent sign 127 01111111 7Fh DEL

Extended ASCII codes

Below are the extended ASCII codes for character codes 128 through 255. This table uses ISO 8859-1 or ISO Latin-1 encoding. Codes 128-159 contain the Microsoft Windows Latin-1 extended characters. Other variations exist, but this is the most commonly used set of character codes.

No. Binary Hex ASCII Description 128 10000000 80H Euro sign 129 10000001 81H 130 10000010 82H, Single Low-9 instruction signs 131 10000011 83H ƒ Small letter F with hooks 132 10000100 84H “Double low-9 quotation brand 133 10000101 85H † Dolch 135 10000111 87H ‡ Doppel-Dolch 136 10001000 88H ˆ Circumflex Akzent 137 10001001 89H ‰ pro Mille Sign 10001110 8EH ž Großbuchstaben Z mit Caron 143 10001111 8fh 144 10010000 90H 145 10010001 91h 150 10010110 96h – en Bindestrich 151 10010111 97h — em Bindestrich 152 10011000 98H ϕ Tilde 153 10011001 99H ™ trademark 154 10011010 9AH Š Small S with Caron 155 109bh Gle Right-Tinging angle Quote brand 156 10011100 9CH œ Small letter OE league line OE league. Ÿ Capital y with diarese 160 10100000 a0h don’t break space 161 101001001 A1h ¡Inverted Exclamation mark mark mark mark mark mark mark mark mark mark markierung markierung ¢ Cent Sign 163 10100011 A3H £ Pfund Zeichen 164 10100100 A4H ¤ Währungszeichen 165 10100101 A5H ¥ Yen Zeichen 166 10100110 A6H â gebrochenen vertikalen BAR 167 10100111 A7H § Abschnittszeichen 168 10101000 A8H ¨ 101010101010101010101001 A9H © COPYRIGHT 17010101010101010101001 A9H Ordinalindikator 171 10101011 Abh «linke Double angle quotes 172 10101100 ACC Sign 173 10101101 ADH Soft Humpen 174 10101110 AEH ® Registered trademark 175 1010111 AFH ϕ overline 176 10110000 B0H degree 177 10110001 B1H ​​± Plus-OR-MINUS SIGN 10100100 B2H ² ² ² ²… 180 10110100 B4H ´ acute 181 10110101 B5H µ microphic 182 10110110 B6H ¶ pilcrow sign 183 10110111 B7H · Middle point 184 B.010 H ¸ Cedilla 185 10111001 B9H ¹ SuperScript One 186 101110 BAH ºCuline ERMAL 187 101111111110 right double angle quotes 188 10111100 BCh ¼ fraction one quarter 189 10111101 BDh ½ fraction one-half 190 1 0111110 Beh ¾ Fraction Three Quarters 191 1011111 BFH ¿Reversed question mark 192 11000000 C0H à upper letter A with grave 193 11000001 C1H á upper letter A with acute 194 11000010 C2H â COMPURENTLE A with Zirkumflex 195 11000100 C4H Ä large letter 196 11,000100 C4H c4H a with diaeresis1 with ring over 198 11000110 C6H Æ capital AE 199 11000111 C7H ç capital C with cedilla 200 11001000 C8H è capital E with grave 201 11001001 C9H É capital E with acute 202 11001010 CAH ê1 EBH020 ê capital EBH00 circumflex1 EBH00 circumflex1 With Diararesiese 204 204 11001100 CCH ì Capital I with grave 205 11001101 CDH í capital I with acute 206 11001110 CEH Î Capital I with circumflex 207 1100111 CFH ï Capital I with DIRENE 208 11010000 D0H ð Capital ETH 209 11010001 D1H ñ Capital N WIT CircumFlex 210 11010010 D2h Ò capital o with circumflex 211 11010011 D3h Ó capital o with acute/td> 212 11010100 D4h Ô capital o with circumflex 213 11010101 D5h Õ capital o with tilde 214 11010110 D6h Ö Capital o with dianeresis 215 11010111 D7H × multiplication sign 216 11011000 D8H Ø Capital O with slash 217 11011001 D9H ù Capital U with Grave 218 11011010 DAH ú Capital U with scoot Þ Large Dorn 223 11011111 DFH ß Small letter Ess-Zed 224 11100000 E0H à Small letter A with grave 225 11100001 E1H á small letter A with acute 226 11100010 E2H â Small letter A with circum flex 226 small letter a with circum flex 227 11100100 E4H Ä a small register Diärese 229 11100101 E5H Å small letter A with ring above 230 11100110 E6H Æ Small letter AE 231 11100111 E7H ç small letter c with Cedille 232 11101000 E8H è small letter e with grave 233 11101001 E9H é Small letter E with acute 234 111010 EAH ê Kleinbucht diaeresis 240 11110000 F0H ð lower case 241 11110001 F1H – lower case N with tilde 242 11110010 F2H ò lower case O with Gr ab 243 11110011 F3H Ó Kleinbuchstaben O mit Akut 244 11110100 F4H ô Unterzugängern Unterzugänge ONSCHUSSE O MENDEFLEFEL OFFLEX 245 111101110100H with tilde 246 11110110 F6h ö lowercase o with diaeresis 247 11110111 F7h ÷ division sign 248 11111000 F8h ø lowercase o with slash 249 11111001 F9h ù lowercase u with grave 250 11111010 FAh ú lowercase u with acute 251 11111011 FBh û lowercase u with circumflex 252 11111100 FCh ü small u with diaeresis 253 11111101 FDh ý small y with acute 254 11111101 FDh ý small y with acute 254 11111110 FEh þ small thorn 111 1 FFy1 mithäre 111ÿs

binary numbers

A computer number system consisting of 2 digits, 0 and 1. It is sometimes called base-2.

Since computers don’t have 10 fingers, counting in the computer itself is done with only 2 digits: 0 and 1 (or “on” and “off” or “false” and “true”).

Hexadecimal numbers

The hexadecimal system (Hex for short) uses numbers from 0 to 15. It starts like the decimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, but then comes A, which equals 10 and then B, C, D, E and F (which of course equals 15). The next number is 10, which is 16 decimal and so on….

Since it can be impossible to distinguish between a hex number and a decimal number (is the “25” a decimal 25 or is it 25 in hexadecimal, which corresponds to a decimal 37?), it is common to put a lower case “h” after each hexadecimal number “ to put. So 25 is a decimal number and 25h is a hexadecimal number.

ASCII

ASCII stands for American Standard Code for Information Interchange. It is a standard defined in 1963 to allow computers to exchange information regardless of manufacturer.