The rules of binary addition are as follows:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0 with a carry-over of 1

 + 0 1 0 0 1 1 1 10

“Carry-overs” of binary addition are performed in the same manner as in decimal addition. With the help of the above rules addition of three or more binary numbers can be worked out but this has little use in digital computers.

For addition of fractional binary numbers, the binary point of the two numbers are placed one below the other just like the decimal points and the usual rules are followed.

A clear concept on few examples will make the procedure of binary addition:

Find the sum of the following numbers:

i) 10101 and 11011

Solution:

10101 and 11011

1 1 1 1      Carry overs

1 0 1 0 1

1 1 0 1 1

1 1 0 0 0 0

ii) 11001 and 111

Solution:

11001 and 111

1 1 1 1      Carry overs

1 1 0 0 1

1 1 1

1 0 0 0 0 0

iii) 10101.101 and 1101.011

Solution:

10101.101 and 1101.011

1 1    1 1   1 1     Carry overs

1 0 1 0 1 . 1 0 1

1 1 0 1 . 0 1 1

1 0 0 0 1 1 . 0 0 0

iv) 111.0111 and 10011.001

Solution:

111.0111 and 10011.001

1 1 1      1 1       Carry overs

1 1 1 . 0 1 1 1

1 0 0 1 1 . 0 0 1

1 1 0 1 0 . 1 0 0 1

• Why Binary Numbers are Used
• Binary to Decimal Conversion
• Conversion of Numbers
• Hexa-decimal Number System
• Conversion of Binary Numbers to Octal or Hexa-decimal Numbers
• Octal and Hexa-Decimal Numbers
• Signed-magnitude Representation
• Arithmetic Operations of Binary Numbers