Binary Multiplication

There are two different methods of solving binary multiplication. 

1. Using long multiplication method.
2. Using conversion method.

Worked Example 4.3.1:

Calculate the product of 1011_two and 101_two 

Solution 

1st Method:

Using long multiplication:

  

Remember the rules for addition:

• 1 + 0 = 1 
• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 1 = 10 
• 1 + 1 + 1 = 11

2nd Method:

Solving the same question using conversion

1011_two × 101_two 

Convert the numbers to base 10 and multiply. Then convert the result to base 2 

1011_two = 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰ 

= 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 

= 8 + 0 + 2 + 1 

= 11_ten 

Also, 

101_two = 1 × 2² + 0 × 2¹ + 1 × 2⁰ 

1 × 4 + 0 × 2 + 1 × 1 

4 + 0 + 1 

= 4 + 1 = 5_ten 

∴ 1011_two × 101_two  = 11_ten × 5_ten

= 55_ten. 

Now we can convert 55_ten to base two

 55_ten = 110111_two

∴ 1011_two × 101_two = 110111_two