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.
| WORKINGS | EXPLANATION |
| 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.
| WORKINGS | EXPLANATION |
| 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
| WORKINGS | EXPLANATION |
| 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
| WORKINGS | EXPLANATION |
| 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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