Computer Calculators

Hexadecimal Calculator

This tool can be used in the calculator mode for performing algebraic operations using hex numbers (add subtract multiply divide hexadecimals).

Hexadecimal Calculator

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Table of contents

What are hexadecimal numbers?
Conversion to and from hexadecimal numbers
Hexadecimal to decimal
Decimal to hexadecimal
How to do HEX addition?
How to multiply HEX values?
Hex division

What are hexadecimal numbers?

Hexadecimal or hexadecimal numbers is a number that has been expressed in the hexadecimal place numeral system. It has a base of 16 and uses 16 symbols. These include the numbers 0-9 and the letters A, B, C, D, E, and F to represent values between 0 and 15. Small-case letters A through F can also be used. For example, 10 in decimal is A in hex, 100 in decimal is 64 in hex, while 1,000 in decimal is 3E8 in hex. Hex numbers can have signed just like decimal numbers. For example, -1e equals -30 in decimal.
Hex numerals are mainly used in computing by programmers, software engineers, and computer system designers as a convenient representation of the underlying binary systems. These occupations will most likely require a hex converter or hex calculator.
They would be encountered by an ordinary user browsing the internet. These special characters are encoded in URLs as a hex number, e.g. %20 is for 'space' (blank). Many web pages also contain special characters in HTML according to their hexadecimal numerical character references (&#x ), for example. The Unicode form a single quotation mark is '. This is the Unicode for a single quotation mark (').
The hexadecimal number systems (Hexa) function almost identically to binary and decimal systems. It uses a base instead of 10 or 2, respectively. HEX uses 16 numbers, including 0-9, and the decimal system's 10 and 2 floors. However, it also uses the letters A, B, C, D, E, and F to represent the numbers 10-15. Each hex digit is 4 binary digits called nibbles. This makes it easier to represent large binary numbers.
The binary value 10101010101010101010101010101010101010101010101010101010101010 is represented in HEX as 2AA. This allows computers to compress large binary numbers in a way that is easy to convert between the two systems.
Here are some examples of conversions between binary, hex, and decimal values.
Decimal Hex Binary
0 0 0
1 1 1
2 2 10
3 3 11
5 5 101
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
50 32 110010
63 3F 111111
100 64 1100100
1000 3E8 1111101000
10000 2710 10011100010000
Converting decimal is possible by understanding the place value of the various number systems. You will notice that the conversion between decimal decimal decimal and Hex is almost identical to the conversion between binary decimal. The ability to convert either should make it easy. You can perform hex functions with the base of 16, as we have already mentioned. This means that every place value of 2AA is a power 16 for the value 2AA. Starting at the right, starting from the left, the first A represents the "ones", which is 16 0. 16 is the second letter A from the right. 1 16 is represented by the 2 and. 2 . Remember that A in hex equals 10 in decimal.

Conversion to and from hexadecimal numbers

Conversion doesn't change the actual number, but it does alter its form. You can quickly and easily convert both types of numbers using our converter. You don't need to do both conversion or calculation simultaneously

Hexadecimal to decimal

Every position in a Hexadecimal numeral is a power 16 just like each decimal number position is a power 10. The decimal number 20 is therefore 2 * 101 + 0,0 * 100 = 20. The decimal number 20 is 2 * 161 + 1 * 160 = 32 in Dec. The number 1E is also 1 * 16 + 14 1 = 30 in decimal.
To convert HEX to decimal, first take each position and then convert it to decimal. 9 is 9, B is converted into 11, and then each position is multiplied by 16 to get the power of the position number. This is done by counting from left to right, starting at zero. Our exponent calculator might be useful if you have to calculate large exponents such as 168.

Decimal to hexadecimal

This is because we're going from a higher to a lower base. Let's say that the number we wish to convert from decimal into hex is X. Start by finding the largest power 16 =X. Next, determine the number of times that power 16 is converted into X. Denote it with E. The remainder should be denoted by Y1.
Continue the steps above using Yn for a starting value, until 16 is greater than the remaining value. Next, assign the 160 positions to the remainder. Finally, assign each value Y1...n its position. You will now have your value.

How to do HEX addition?

Decimal addition has the same rules for HEX addition, with the exception of the addition numerals A, B, and C. If these numbers have not been stored in memory, it may be useful to have the equivalent decimal values of A through F on hand. Below is an example of addition.


Subtraction can also be done in the same manner as adding. This is accomplished by performing the operation while converting between decimal and hex values. Borrowing is the most important difference between decimal and subtraction.  The "1" in hex is 16 decimal, rather than the 10 decimal when borrowing.  The reason is that the column being borrowed is 16 times bigger than the borrowing column. This is the same reason why the 1 in decimal represents 10. This is important to note and the conversions of letter numbers A-F should be done with care. Hex subtraction is no more difficult than decimal subtract.

How to multiply HEX values?

It can be challenging to do multiplication because of the difficulty in converting between decimal (hex) and decimal (decimal) operations. The numerals are generally larger so it takes more effort. It can be useful to have a hexadecimal multiplier table (one is provided below). Manual conversions between decimal will be required for each step.

Hex division

Long division is exactly like long division in decimal. However, multiplication, as well as subtraction, are done in hex. You can also convert decimal to perform long division, and then return once the conversion is complete. A hexadecimal table for multiplication (one is provided below), would be helpful when conducting division.
Parmis Kazemi
Article author
Parmis Kazemi
Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.
Hexadecimal Calculator English
Published: Tue Dec 21 2021
Latest update: Fri Aug 12 2022
In category Computer calculators
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