# Hexadecimal and Binary

## Understanding Hexadecimal and Binary

**Hexadecimal**is a base-16 number system. It’s made up of 16 symbols: the numbers 0-9 and the letters A-F.- The letter A represents the decimal number 10, B represents 11, and so on, up until F which represents 15.
- The use of hexadecimal significantly reduces the length of binary numbers, making them easier to read and understand.
- In computing, hexadecimal often represents binary numbers, as each hexadecimal digit can represent four binary digits or bits.
- This four-bit group is also known as a
**nibble**, and two nibbles make a**byte**.

## Binary to Hexadecimal Conversion

- To convert binary to hexadecimal, you group the binary number into nibbles from the right and then convert each nibble separately into its hexadecimal equivalent.
- For example, the binary number
`10110011`

can be split into the nibbles`1011`

and`0011`

. These in turn are equivalent to the hexadecimal digits B and 3 respectively. So`10110011`

in binary is`B3`

in hexadecimal.

## Hexadecimal to Binary Conversion

- To convert hexadecimal to binary, you convert each hexadecimal digit into its four-bit binary equivalent.
- For example, the hexadecimal number
`A9`

is made up of the digits`A`

and`9`

.`A`

is`1010`

in binary and`9`

is`1001`

in binary. So`A9`

in hexadecimal is`10101001`

in binary.

## Practical Use of Hexadecimal

- Hexadecimal is extensively used in programming and computing because it is concise and easier to read than binary, particularly when dealing with large numbers or colour codes.
- It also provides an easily readable and writable representation of binary data, while still maintaining a strong correlation to the binary structure, thereby enabling easier debugging and examination of system-level data.