Multiplication of Binary Numbers

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A tutorial on how to multiply binary numbers, along with examples, exercises and answers is presented.

let us first add binary numbers with one digit
0 x 0 = 0
0 x 1 = 1
1 x 0 = 1
1 x 1 = 1
The above simple additions are similar to those of decimal.

We now multiply numbers with more than one digit: 1 0 1 1 x 1 0 0 1

1) The multiplication of binary numbers is similar to the multiplication of decimal numbers.

1 0 1 1
x
1 0 0 1
____ ____ ____ ____
1 0 1 1
0 0 0 0
0 0 0 0
1 0 1 1
___ ___ ___ ___ ___ ___ ___
1 1 0 0 0 1 1

The multiplication of binary numbers is done by shifting by one bit and adding. It can be easily checked that 1011 which is 11 in decimal multiplied by 1001 which is 9 in binary gives 99 which is 1100011 in binary.

Exrecises

A) Multiply the binary numbers.
  1. 111 x 11
  2. 1011 x 111
  3. 10101 x 1101
  4. 100011 x 1100011 (you need to know that 1 + 1 + 1 + 1 = 100 carry 10)

Answers to Above Exercises

  1. 111 x 11 = 10101
  2. 1011 x 111 = 1001101
  3. 10101 x 1101 = 100010001
  4. 100011 x 1100011 = 110110001001


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Updated: 5 November 2010

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