Binary

• Bit​ - This is the name for a single binary digit (e.g. 0 or 1)​
• Byte​ - A byte is the name given to 8 bits​
• Nibble​ - A nibble is half a byte (4 bits)

What is binary?

Binary (also known as base-2) is a number system which only uses 0s and 1s​.

This is a useful number system to use in computer science because a computer is made from millions of tiny components which only understand a state of ON or OFF​. Any form of data needs to be converted to binary to be processed by a computer, once in this format data is processed using [[ logic gates ]] and stored in small pieces of memory called [[ registers ]].

This means we can easily match the state of the computer to a binary value​:

• A switch set to ON equals 1
• A switch set to OFF equals 0

By combining millions of these ON and OFF signals together, we can program a computer to think!

This is different to denary (also known as base-10 or decimal), the name of the number system you use every day​, which uses the numbers 0 to 9​.

Example of a binary number

Consider the 8-bit number 11101110, this can be re-written in a table as follows:

A place value is written above each of the bits, increasing by powers of 2 (1, 2, 4, 8, etc…). The value of this binary number can be calculated by adding together all place values where the bit is equal to 1.

128 + 64 + 32 + 8 + 4 + 2 = 238

Counting in 4-bit binary

In the table below you can see all possible 4-bit binary values 0000 to 1111, in denary this is equivalent to 0 to 15.