Binary Subtraction

Worked Example 4.2.1:

Subtract 

a. 1011_two from 10101_two 
b. 111010_two – 11011_two 

a. 1011_two from 10101_two 

Note: First column by the right 1 – 1 = 0 

Second column: 0 – 1 is not possible, so we borrow 1 from the third column to give 10. So, 10 – 1 = 1 

Third column: 1 is reduced to 0 because it was lent to the second column. ∴ 0 – 0 = 0 

Fourth column: 0 – 1 is not possible, so borrow 1 from the fifth column to give 10. So, 10 – 1 = 1 

Fifth column: 1 is reduced to 0 because it was lent to the fourth column.

⇒ 10101_two – 1011_two = 1010_two 

b. 111010_two – 11011_two 

First column by the right 0 -1 is not possible so we borrow 1 from the second column to give 10. So, 10 – 1 = 1 

Second column: subtract 1 that was borrowed 1 – 1 = 0. What we have left is 0 – 1 which is not possible, so we borrow 1 from the third column to give 10. So, 10 – 1 = 1 

Third column: 0 – 1 = -1, -1 is less than 0 so we borrow 1 from the fourth column to give 10 – 1 = 1

Fourth column: subtract 1 that was borrowed 1 – 1 = 0. What we have left is 0 – 1 which is not possible, so we borrow 1 from the fifth column to give 10. So, 10 – 1 = 1 

Fifth column: subtract 1 that was borrowed 1 – 1 = 0. What we have left is 0 – 1 which is not possible, so we borrow 1 from the sixth column to give 10. So, 10 – 1 = 1 

Sixth Column: subtract 1 that was borrowed 1 – 1 = 0

⇒ 111010_two – 11011_two = 11111_two