Intro

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

Binary addition

Lets start with basic decimal addition.

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.

Onto binary addition

Binary addition is the same concept. Except for your using binary numbers 1 and 0. Answer 5159

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.

You can double check

1011 = 11

1011 = 11

11 + 11 = 22

Answer 10110 = 22