Binary addition

Binary can be added together. Let's add 7 and 14 together as an example.

7

Decimal 16 8 4 2 1
Binary 0 0 1 1 1

14

Decimal 16 8 4 2 1
Binary 0 1 1 1 0

21

Decimal 16 8 4 2 1
Binary 1 0 1 0 1

The rules for addition are described below:

0+0 0
1+0 1
0+1 1
1+1 0 carry 1
1+1+1 1 carry 1

7 and 14 are 0111 and 1110. We add the first digits, this gives us 1, since 1 + 0 = 1.

 
0111
1110
1

Next, we add 1 and 1. This gives us 2, which in binary is 10. So we write down 0, and carry the 1.

1
0111
1110
01

Now, since we carried a bit, we have 3 bits to use. This gives us 3, which is represented as 11. So we write down 1 and carry the other 1.

1
0111
1110
101

Since we carried 1, we need to add 1 + 0 + 1, which equals 2. This in binary is 10, so we write that down.

 
0111
1110
10101

This seems pretty simple, but binary addition overflow can occur.

Author: Matei Cotocel

Created: 2021-11-13 Sat 19:37

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