Binary Arithmetic Operations – Subtraction

This operation is similar to the basic arithmetic subtraction performed on decimal numbers in Maths. Hence, when we subtract 1 from 0, we need to borrow 1 from the next higher order digit, to reduce the digit by 1 and the remainder left here is also 1.

When you borrow a number during subtraction, it becomes the number of the base you are subtracting from.

For example, in Base 2 if you borrow a number the number you borrow becomes 2.

Worked Example 2.2.1:

Subtract the following:

i. 1001_two from 11001_two
ii. 11011_two  from  111010_two
iii. 1101_two – 111_two
iv. 10001_two – 1110_two
v. 1111_two – 101_two

Solution

i. 1001_two from 11001_two

Explanation

1st Column (from right to left): 1 – 1 = 0. Write 0.