Lesson 4, Topic 2
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# Binary Subtraction

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Note

0 – 0 = 0
1 – 0 = 1
1 – 1 = 0
10 – 1 = 1
11 – 1 = 10

### Example:

Subtract

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

a. 1011two from 10101two

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

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

Third column: 0 – 0 = 0

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

⇒ 10101two – 1011two = 1010two

b. 111010two – 11011two

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. then 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. then 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. then 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

⇒ 111010two – 11011two = 11111two

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