Hexadecimal Calculator
Use our Hex Calculator for performing Addition, Subtraction, Multiplication and Division of hexadecimal numbers. You can perform algebraic operations with hex numbers using this hexadecimal calculator. You can also use our Hexadecimal converter to convert base from Hex to Binary, Decimal, Octal etc.
Explore other calculators or unit converters or try out our Hexadecimal Calculator and learn more about Hexadecimal .
Solution:
Hexadecimal Calculator Details
What is Hexadecimal Number?
A Hexadecimal (Hex) number is a number expressed in the base-16 numeral system (hex numeral system). Hexadecimal numbers are represented by 16 symbols. Symbols “0”–”9″ to represent values 0 to 9, and “A”–”F” to represent values from 10 to 15.
Hex Arithmetic Operations – Add, Subtract, Multiply and Divide
Addition
Addition of hexadecimal is similar to decimal addition.
When the result of an addition of digits exceeds the maximum permissible values then you have to carry the excess amount divided by the radix (16) to the digit on left, so that it can be added to the next place value.
8AC16 + B7E16
| 1 | 1 | ||
| 8 | A | C | |
| + | B | 7 | E |
| 1 | 4 | 2 | A |
- C16 + E16 = 1A16 1 will be carry forward to next column
- 116 + A16 + 716 = 1216 1 will be carry forward to next column
- 116 + 816 + B16 = 1416
Subtraction
Subtraction of hexadecimal is similar to addition, instead of carry the numbers borrow from left column (more significant digit).
8AC16 + B7E16
| A | 16 | ||
| B | A | 3 | |
| – | 8 | B | 3 |
| 2 | F | 0 |
- 316 – 316 = 0
- A16 – B16 = F16 As A is smaller than B, so borrow is required, therefore we will subtract 1 from the more-significant digit and add a decimal 16 to the digit being borrowed to
- As we have borrowed from B16 so it will become A16, therefore A16 – 816 = 216
Conversion to and from other Numeral Systems
Hexadecimal to Decimal
Refer to our Number Base Converter to know about conversion from Decimal to Hexadecimal. Hexadecimal to Decimal conversion (from base 16 to Base 10) is simply inverse of the Decimal to Hexadecimal conversion process.
Multiply the digits (bits) of the hex number starting with the least significant (rightmost) bit with 16n and then add all of them. Here n is the position of the digit starting from the right assuming the position of the rightmost digit as 0.
Converting 15A from Base 16 to Decimal
1 * 162 + 5 * 161 + A (10) * 160 = 346 in Decimal
Hexadecimal to Binary
Hexadecimal can be converted to Binary by converting Hexadecimal to Decimal and then converting the Decimal number to Binary.
As Hexadecimal base 16 is power of 2, Hexadecimal can also be converted directly to binary. To convert hexadecimal to binary, you have to simply substitute the corresponding binary digits of each hexadecimal bit.
3C16 = 0011 1100 = 1111002
Refer to our Binary Base Calculator and Conversion to know about conversion from Binary to Hexadecimal.
Hexadecimal to Octal
Hexadecimal can be converted to Octal by converting Hexadecimal to Decimal and then converting the Decimal number to Octal.
As both Hexadecimal base 16 and Octal base 8 are power of 2, Hexadecimal can also be converted Octal by first converting to binary.
Convert Hexadecimal to Binary by above method and then to convert a binary number to Octal, divide the binary in groups of 3 bits starting from left.
3C16= 0011 11002 = 1111002 = 111 1002 = 748
Refer to our Octal Base Calculator and Conversion to know about conversion from Octal to Hexadecimal.