What is the Hexadecimal System?

The hexadecimal number system (hex) functions virtually identically to the decimal and binary systems. Instead of using a base of 10 or 2 respectively, it uses a base of 16. Hex uses 16 digits including 0-9, just as the decimal system does, but also uses the letters A, B, C, D, E, and F (equivalent to a, b, c, d, e, f) to represent the numbers 10-15.

Every hex digit represents 4 binary digits, called nibbles, which makes representing large binary numbers simpler. For example, the binary value of 1010101010 can be represented as 2AA in hex. This helps computers to compress large binary values in a manner that can be easily converted between the two systems.

Hex/Decimal Conversion Table

How Hexadecimal Conversion Works

Converting between decimal and hex involves understanding the place values of the different number systems. The hexadecimal system uses base 16, which means each digit represents a power of 16.

To convert decimal to hex:

1. Find the largest power of 16 that is less than or equal to the number
2. Divide the number by this power of 16 to get the quotient
3. Multiply the quotient by the power of 16 and subtract from the number
4. Repeat with the remainder until the result is 0
5. The hex number is the sequence of quotients written from left to right

Hexadecimal Addition

Hex addition follows the same rules as decimal addition with the only difference being the added numerals A through F.