Binary is formed of 2 digits either a 1 or a 0.

Denary is the numbers that we see every day like 1,2,3,4,5,6,7,8,9,10 etc. But how do we convert binary to denary, add binary and subtract binary?

### Converting Binary and Denary

128 64 32 16 8 4 2 1

0 1 0 0 0 1 0 0 = 64+4= 68

01000100 in Binary = 68 in Denary.

**Adding Binary**

001001 = 9

100101 = 37

101101 = 46

37+9=46

To add binary you simply add a 1 when there is a 0 in the other number and if there is already a 1 there, you put 0 and carry the 1 to the next number. If at the end of the number you have any left overs you simply ignore it.

### Subtracting Binary

Subtracting Binary is harder and there are 2 ways you can go about it.

a. you do a 1s compliment and a 2s compliment and add the results

b. you convert the numbers to binary, subtract them and convert them back to binary

Option b often takes longer and you may not have enough time to do that in an exam

A.

10011 = 19

01111 = 15

1s compliment – invert the number your subtracting

0 1 1 1 1

1 0 0 0 0

2s compliment – +1 to this new binary number

1 0 0 0 1

Then add them both

10011

10001

00100

remove the left over 1

00100

19-15+4

00100 = 4

16 8 4 2 1

0 0 1 0 0 = 4