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

Binary Numbers

  • 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
  • Radix Complement
  • Diminished Radix Complement
  • Arithmetic Operations of Binary Numbers


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