Binary Addition

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Topic Content:

Rules of Binary Addition
Worked Examples

It is possible to add, subtract and multiply binary numbers in a similar way to base ten numbers. The main things to remember in base two are the following

Below are rules of binary addition:

1 + 0 = 1
0 + 0 = 0
0 + 1 = 1
1 + 1 = 10
1 + 1 + 1 = 11

Rule	A + B	Sum (What we write down)	Carry (What we write carry)
1.	0 + 0	0	0
2.	0 + 1	1	0
3.	1 + 0	1	0
4.	1 + 1	0	1
5.	1 + 1 + 1	1	1

Worked Example 4.1.1:

Add 111_two to 11_two

⇒ 111_two + 11_two= 1010_two

Explanation:

First column by the right: 1 + 1 = 10

Write the 0 and carry 1 {forward (1)}

Second column in the middle: (1) carried + 1 + 1 = 11.

Write down 1 and carry 1 {forward (1)}

Third column: 1 carried + 1 = 10

Worked Example 4.1.2:

Add 1011_two to 1101_two

Solution

First column by the right: 1 + 1 = 10 write down 0 and carry 1

Second column: the 1 carried forward +1 write down 0 carry 1

Third column: the 1 carried forward from second column +1, write down 0 and carry 1

Fourth column: 1 carried from third column + 1 + 1 = 11

⇒ 1011_two + 1101_two = 11000_two

JSS1: MATHEMATICS - 1ST TERM

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Binary Addition

Topic Content:

Worked Example 4.1.1:

Worked Example 4.1.2: