Addition Of Binary Numbers

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.

WORKINGSEXPLANATION
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.

WORKINGSEXPLANATION
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

WORKINGSEXPLANATION
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

WORKINGSEXPLANATION
11
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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