Addition of binary numbers, or numbers in base two, follows the same method as with the addition of other base numbers.
In this lesson, you will learn the step-by-step method for the addition of binary numbers, or numbers in base two.
Question on the addition of binary numbers
Let’s take an example:
Question:
Add 1112 and 1102
STEP 1.
Position the numbers
Arrange the numbers exactly how you would arrange them in your normal addition.
WORKINGS | EXPLANATION |
1112 1102 ______ | You can decide not to include the base beside the numbers but remember the base for subsequent steps below. |
STEP 2.
Start your addition
Start from the back as you do in your normal addition.
WORKINGS | EXPLANATION |
111 110 _____ ___,1 | 1 + 0 = 1 The answer 1 is smaller than our base 2, so there is no need for breaking it down. |
STEP 3.
Continue your addition
WORKINGS | EXPLANATION |
111 110 _____ _,01 | 1 + 1 = 2 The answer 2 is equal to our base 2, so we use repeated division to break 2 down to (1, 0). Write down the last digit (0) and carry (1) over to the next addition. |
STEP 4 — final answer
Finish your addition
WORKINGS | EXPLANATION |
1¹11 1 1 0 ______ 1101 | 1 + 1 = 2 2 + 1 (carried over) = 3 The answer 3 is bigger than our base 2, so we use repeated division to break 3 down to (1, 1) Write down the entire number (1, 1) because there is no next addition to carry anything over to. |
FINAL ANSWER:
1112 + 1102
= 11012
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