# Decimal and Hexadecimal

A gentle  introduction to hexadecimal (base 16).

### Decimal numbers

In our standard decimal system each digit (which can be 0,1,2,3,4,5,6,7,8,9) in a number represents a power of ten in that place:

The hexidecimal (base 16) system is similar, except that each digit represents a power of 16 in that place.

Because a digit can have values greater than 9, there are additional digit symbols allowed in hex:

• A (10), B (11), C (12), D (13), E (14) and F (15)

To convert a decimal number to hex, you remove multiples of those powers of 16 as shown below.

### Binary numbers

In the binary (base 2) system, each digit is a power of two, and the digits are just 0 and 1.

It's easy to translate a hexadecimal number into binary because you can decompose each hex digit into its 4 bits.

The benefit of using hexadecimal instead of binary, is that hex is much shorter to write, but still lets us easily determine the value of specific bits.

### Octal numbers

Another popular base in the computer world is octal – (base 8) where each digit is a power of 8, and digits are 0, 1, 2, 3, 4, 5, 6, 7.

Octal is more compact than binary, but less compact than either decimal or hexadecimal.

• No labels