Binary Numbers Addition

This is my first post on binary arithmetic. In this post, I will explain the addition of binary numbers with some solved examples.

Key Questions:

• How to perform binary addition?
• How to perform addition on fractional binary numbers?

Binary Addition Rules

Binary addition is the same as it is in decimal numbers. It's a simple and easy task. Have a look at the table. Here are some rules for the addition of binary numbers.

A+B	Result	Carry
0+0	0	0
0+1	1	0
1+1	10	1
10+1	11	1

Binary Addition Solved Examples:

Example#01:0101111011)2+11111111000)2

A=0101111011

B=11111111000

A			0	1	0	1	1	1	1	0	1	1
B	+	1	1	1	1	1	1	1	1	0	0	0
Result	1	0	0	1	0	1	1	1	0	0	1	1
Carry		1	1	1	1	1	1	1	1	0	0	0

Check your results:

You can check results by converting each binary number into decimal and add them. I check my results using this online converter.

0101111011)2=379)10

11111111000)2=2040)10

100101110011)2=2419)10

Answer 0101111011)2+11111111000)2=100101110011)2

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Example#02:101010111)2+1111000011)2

A=101010111

B=1111000011

A			1	0	1	0	1	0	1	1	1
B	+	1	1	1	1	0	0	0	0	1	1
Result	1	0	1	0	0	0	1	1	0	1	0
Carry		1	1	1	1	0	0	0	1	1	1

Check your answer:

101010111)2         =343)10

1111000011)2      = 963)10

10100011010)2=1306)10

Answer: 101010111)2+1111000011)2=10100011010)2

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Example#03:100111.1100)2+111011.1011)2

A=100111.1100

B=111011.1011

A		1	0	0	1	1	1	.	1	1	0	0
B	+	1	1	1	0	1	1	.	1	0	1	1
Result	1	1	0	0	0	1	1	.	0	1	1	1
Carry		1	1	1	1	1	1		1	0	0	0

Check your answer:

100111.1100)2=39.75)10

111011.1011)2=59.6875)10

1100011.0111)2=99.4375)10

Answer:1100011.0111)2

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Example#04: add 01011101,11110000,11001100,11011110

Add two numbers at a time. add the third number and then the fourth number.

A=01011101

B=11110000

C=11001100

D=11011110

Step 1:

A		0	1	0	1	1	1	0	1
B	+	1	1	1	1	0	0	0	0
Result 1	1	0	1	0	0	1	1	0	1
Carry		1	1	1	1	0	0	0	0

Check your results:

01011101 = 93)10

11110000 = 240)10

101001101 = 333)10

Step 2:

Result 1		1	0	1	0	0	1	1	0	1
C		+	1	1	0	0	1	1	0	0
Result 2	1	0	0	0	0	1	1	0	0	1
Carry		1	1	1	0	0	1	1	0	0

Check your results:

101001101 = 333)10

11001100 = 204)10

1000011001 = 537)10

Step 3

Result 2	1	0	0	0	0	1	1	0	0	1
D	+		1	1	0	1	1	1	1	0
Result 3	1	0	1	1	1	1	0	1	1	1
Carry		0	0	0	0	1	1	0	0	0

Check your results:

1000011001 = 537)10

11011110 = 222)10

1011110111 = 759)10

Answer: 1011110111)2