Addition of number bases that are not binary, or numbers from base 3 upward, follow the same method as with the addition of binary numbers.

In this lesson, you will learn the step-by-step method for the addition of number bases that are not binary.

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

Question on the addition of number bases that are not binary

Let’s take an example:

QUESTION:
Add 314₅ and 24₅

STEP 1.

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

WORKINGS	EXPLANATION
314₅ +24₅ ______	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 would do in your normal addition.

WORKINGS	EXPLANATION
314 +24 _____ ___3	4 + 4 = 8 The answer 8 is bigger than our base 5, so we use repeated division to break 8 down to (1, 3). Write down the last digit (3) and carry (1) over to the next addition.

WORKINGS	EXPLANATION
31¹4 +2 4 _____ _,4 3	1 + 2 = 3 3 + 1 (carried over) = 4 The answer 4 is smaller than our base 5, so there is no need for breaking it down.

WORKINGS	EXPLANATION
314 +24 _____ 343	3 + nothing = 3 The answer 3 is smaller than our base 5, so there is no need for breaking it down.

FINAL ANSWER:
314₅ + 24₅
= 343₅

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