Subtraction Of Binary Numbers

Subtraction of binary numbers refers to the subtraction of numbers in base two. The method here is similar to the subtraction of other base numbers.

In this lesson, you will learn the step-by-step method in the subtraction of binary numbers or numbers in base two.

BONUS: A link to practice questions on number bases is included at the end of this lesson.

Question on the subtraction of binary numbers

Question:

Solve 11012 – 1112

STEP 1.

Position the numbers

Arrange the numbers exactly how you would arrange them in your normal subtraction.

WORKINGSEXPLANATION
11012
– 111 2
_______
You can decide not to include the base beside the numbers but remember the base for subsequent steps below.

STEP 2.

Start your subtraction

Start from the back as you would do in your normal subtraction.

WORKINGSEXPLANATION
1101
– 111
_______
_____0
1 – 1 = 0

The answer 0 is smaller than our base 2, so there is no need for breaking it down.

STEP 3.

Continue your subtraction

WORKINGSEXPLANATION
1101
–111
______
____0
0 – 1 = it is impossible to remove 1 from 0, so we borrow.

NOTE! In subtraction of number bases, what you borrow takes the value of the base.
100²1
–1 1 1
_______
___1 0
0 + 2 (borrowed) = 2
2 – 1 = 1

Since we are calculating in base 2, the 1 we borrowed became 2.

STEP 4 — final answer

Finish your subtraction

WORKINGSEXPLANATION
1021
–111
_______
___10
0 – 1 = it is impossible to remove 1 from 0, so we borrow.

NOTE! Once again, what you borrow takes the value of the base.
00²21
–1 1 1
_______
_1 1 0_
0 + 2 (borrowed) = 2
2 – 1 = 1

We are still calculating in base 2, so the 1 we borrowed became 2.

FINAL ANSWER:

11012 – 1112

= 1102

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