Multiplication Binary

In this article, we are going to discuss multiplication binary. In mathematics or computer science, all our computations are based on decimal system or Base 10 (denary) system. Some of the other number systems is base-2, base-3, base-4, etc. Here, we are going to see about the binary system. The binary numbers have two digits and they are 0, 1. Any number in binary is written using only these two digits. Now we are going to learn the concepts and the example problems for binary multiplication.

 

Truth table for binary number systems:

 

 

The following table shows the binary values of the equivalent decimal numbers.                  

 

Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111

 

The following truth table to easily perform the addition operations of the given two binary numbers.

 

`^+2` 0 1
0 0 1
1 1 10

 

 

Truth table for binary multiplication:

 

 

`^xx 2` 0 1
0 0 0
1 0 1

 

 

Truth table for binary subtraction:

 

 

A B BORROW A-B
0 0 0 0
1 0 0 1
0 1 1 1
1 1 0 0

 

 

 

Truth table for binary division:

 

 

 

A B `A/B`
0 0 0
0 1 0
1 1 1

 

Note:

    Whatever may be the number system the process of addition is the same. When the result of binary addition exceeds the value 1 then these will be carry over as per the above truth table.

  

Examples for multiplication binary:

 

Example 1:      

Multiplication binary: `1011_2 xx 11_2` by using truth table.

Solution:

     Given:

         `1011_2 xx 11_2` .

To perform the binary multiplication:

             1 0 1 1
                  1 1
           -------------
          1  0  1  1
      1  0  1  1
    -------------------
  1  0  0  0  0 1
  -------------------

Steps for binary multiplication:

     `rArr` The multiplicand 1011 is multiplied by once position from multiplier 11 we get.

                   `1011_2 xx 1_2 = 1011_2` .

            the result of the value is placed under the multiplier 11.

     `rArr`The multiplicant 1011 is multiplied by tens position from multiplier 11 we get.

                   `1011_2 xx 1_2 = 1011_2`.

     the result of the value is placed  under the multiplier of tens positions.

     Now we are going to perform addition of these two results.

Thus the required answer of binary multiplication.

 

Example 2:

 

Multiplication binary: `1011_2 xx 10_2` by using the truth table.

Solution:

     Given:

         `1011_2 xx 10_2` .

To perform the binary multiplication:

              1 1 0 1
                   1 0
            -------------
          0  0  0  0
      1  1  0  1
     -------------------
     1  1  0  1  0
     -------------------

Steps for binary multiplication:

     `rArr` The multiplicand 1101 is multiplied by once position from multiplier 10 we get.

                   `1101_2 xx 0_2 = 0000_2` .

            the result of the value is placed under the multiplier 10.

     `rArr`The multiplicand 1101 is multiplied by tens position from multiplier 10 we get.

                   `1101_2 xx 1_2 = 1101_2`.

     the result of the value is placed under the multiplier of tens positions.

     Now we are going to perform addition of these two results.

Thus the required answer of binary multiplication.