# The learning nerd!

On a mission to learn everything!

# Binary addition and subtraction — February 15, 2015

## Intro

This is a continuation of the learning binary series. Be sure to read learning binary before reading this post.

The basic values column
1000 | 100 | 10 | 1
Example

 1 1 1 5 9 5 + 3 5 6 4 _ _ _ _ 5 1 5 9

We take the first digit and carry that. While the second digit remains below.
The digit you carried is added to the number.
5 + 4 = 9 > 9 Is less then 10 so we don’t carry over.
9 + 5 = 15 > 15 is higher then 10. We need to carry a 1 over into the 100’s column.
1 + 5 + 5 = 11 > 11 is higher then 10. We need to carry a 1 over into the 1000’s column.
1 + 1 + 3 = 5 > 5 is less then 10 so we don’t carry over.

Binary addition is the same concept. Except for your using binary numbers 1 and 0.

#### The five basic addition rules

0 + 0 = 0
1 + 0 = 1
10 + 0 = 10
1 + 1 = 10 > 1 + 1 = 2 > 10 = 2 in binary
10 + 1 = 11

Example

 1 1 1 1 0 1 1 + 1 0 1 1 _ _ _ _ _ 1 0 1 1 0

1 + 1 = 10 > We carry the 1
1 + 1 + 1 = 10 + 1 = 11 > We carry the 1
1 + 0 = 1
1 + 1 = 10 > Since there is no more columns to carry. We put 10.

1011 = 11
1011 = 11
11 + 11 = 22

# Binary subtraction

Example

 3 4 16 3 3 5 6 4 − 2 3 4 9 0 _ _ _ _ _ _ 1 0 0 7 4

4 – 0 = 4
Borrow 1 to make 16 – 9 = 7
Borrow to make 4 – 4 = 0
Borrow to make 3 – 3 = 0
3 – 2 = 1

10074

Onto binary subtraction

#### The four basic subtraction rules

0 – 0 = 0
1 – 0 = 1
1 – 1 = 0
10 – 1 = 1

 0 1 10 10 1 0 1 0 1 − 1 1 1 0 _ _ _ _ _ _ 0 0 1 1 1

1 – 0 = 1
Borrow 1 to make 10 – 1 = 1
Borrow 1 to make 10 – 1 = 1
Borrow 1 to make 1 – 1 = 0
Borrow 0 to make 0

#### You can double check

10101 = 21
1110 = 14
21 – 14 = 7

I hope you enjoy my tutorial on how to subtract and add binary numbers. The next guide in this series will be how to multiply and divide binary numbers.

Categorised as: Binary