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.

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.

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.

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.

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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