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

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● Binary Numbers