# Binary Subtraction

Binary subtraction is also similar to that of decimal subtraction with the difference that when 1 is subtracted from 0, it is necessary to borrow 1 from the next higher order bit and that bit is reduced by 1 (or 1 is added to the next bit of subtrahend) and the remainder is 1.

Thus the rules of binary subtraction are as follows:

0 - 0 = 0

1 - 0 = 1

1 - 1 = 0

0 - 1 = 1 with a borrow of 1

# Binary Subtraction Table

 - 0 1 0 0 1 1 1 0

For fractional numbers, the rules of subtraction are the same with the binary point properly placed.

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

Subtract the following numbers:

i) 101 from 1001

Solution:

101 from 1001

1 Borrow

1 0 0 1

1 0 1

1 0 0

ii) 111 from 1000

Solution:

111 from 1000

1 Borrow

1 0 0 0

1 1 1

0 0 0 1

iii) 1010101.10 from 1111011.11

Solution:

1010101.10 from 1111011.11

1 Borrow

1 1 1 1 0 1 1 . 1 1

1 0 1 0 1 0 1 . 1 0

1 0 0 1 1 0 . 0 1

iv) 11010.101 from 101100.011

Solution:

11010.101 from 101100.011

1         1   1      Borrow

1 0 1 1 0 0 . 0 1 1

1 1 0 1 0 . 1 0 1

1 0 0 0 1 . 1 1 0

• Decimal Number System
• 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