Recap:What is Binary?

In computing, we often use two systems to represent numbers: binary and denary.

The binary system uses only two digits, 0 and 1 because computers only understand this.

While the denary system is the one we use every day, which includes the digits from 0 to 9.

In denary, a number is represented with Units, Tens, hundreds, thousands (Goes up by x10)

e.g. 1000 100 10 1

In binary, a number is represented with 1, 2, 4, 8, 16 .... (goes up by x2)

e.g. 128 64 32 16 8 4 2 1

Each Binary digit, is called a "bit".

E.g. The denary number 64 can be represented in binary (0s and 1s) as 01000000.

How to convert a Denary number to Binary:

E.g. Convert 135 into Binary

Step 1: Write the binary headings.

Headings for 8 bits:

128 64 32 16 8 4 2 1

Step 2: Start from the left-most header.

If the number can be subtracted, but a 1.

Else put a 0.

Continue going right with the remainder.

135 - 128 = 7 (remaining)

128 64 32 16 8 4 2 1

1

7 - 64 will be less than 0, so put a 0.

128 64 32 16 8 4 2 1

1 0

7 - 32? Put a 0.

128 64 32 16 8 4 2 1

1 0 0

7 - 16? Put a 0.

128 64 32 16 8 4 2 1

1 0 0 0

7 - 8? Put a 0.

128 64 32 16 8 4 2 1

1 0 0 0 0

7 - 4 = 3 (remaining)

128 64 32 16 8 4 2 1

1 0 0 0 0 1

3 - 2 = 1 (remaining)

128 64 32 16 8 4 2 1

1 0 0 0 0 1 1

1 - 1 = 0 (remaining)

128 64 32 16 8 4 2 1

1 0 0 0 0 1 1 1

135 into Binary is 10000111

https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/3