Multiplication & Division

Binary multiplication

  is actually much simpler than decimal multiplication. In the case of decimal multiplication, we need to remember 3 x 9 = 27, 7 x 8 = 56, and so on. In binary multiplication, we only need to remember the following,

0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1

Note that since binary operates in base 2, the multiplication rules we need to remember are those that involve 0 and 1 only. As an example of binary multiplication we have 101 times 11,

  101
  x11

First we multiply 101 by 1, which produces 101. Then we put a 0 as a placeholder as we would in decimal multiplication, and multiply 101 by 1, which produces 101.

  101
  x11
  101
1010  <-- the 0 here is the placeholder

The next step, as with decimal multiplication, is to add. The results from our previous step indicates that we must add 101 and 1010, the sum of which is 1111.

  101
  x11
  101
1010
1111

Binary division

  is almost as easy, and involves our knowledge of binary multiplication. Take for example the division of 1011 into 11.

          11   R=10
 11 )1011
        -11
         101
          -11
           10  <-- remainder, R

To check our answer, we first multiply our divisor 11 by our quotient 11. Then we add its' product to the remainder 10, and compare it to our dividend of 1011.

     11
  x 11
     11
   11 
  1001  <-- product of 11 and 11

 1001
 +  10
  1011  <-- sum of product and remainder

The sum is equal to our initial dividend, therefore our solution is correct.

To practice binary addition and subtraction, visit the Practice Exercises page.

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Binary Numbers | Add & Subtract | Multiply & Divide | Exercises | Conversion