How to Add Binary Numbers

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  • 0:04 The Steps
  • 2:47 The Solution
  • 2:52 A Unique Situation
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you'll see that adding binary numbers isn't that difficult. And in some ways, it might be even easier than your regular addition! You'll learn the 3 rules to adding binary numbers and work out a few examples.

The Steps

Binary numbers are numbers written with a base of two, specifically 0 and 1. We normally write numbers with a base of 10 called decimal numbers, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A 0 in binary is a 0 in base 10. A 1 in binary is a 1 in base 10. A 10 in binary is 2 in base 10. A 11 in binary is 3 in base 10.

Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001

This goes on, with each successive number taking on an additional ''1''. As you count, you keep adding more digits, just as you would with other numbers. Computers count using the binary system, so computer programmers and anyone else working with electronics may encounter problems that involve binary calculation. You may need to add 101 and 110 together.

But how does addition in binary work? We'll take our example of 101 and 110 and see just how to do this:

The first step is to recall the rules for binary addition. The rules for binary addition are a bit different than for decimal addition, which is the addition we're familiar with. Binary addition only has three rules:

  1. 0 + 0 = 0
  2. 0 + 1 = 1 or 1 + 0 = 1
  3. 1 + 1 = 10

All you have to remember is that ''0'' and ''0'' make 0. If you have a ''1'' and a ''0'', you'll get 1. If you have two ''1''s, you end up with a 10. And since we are using the binary system, we don't say ten here. As we said, we read the individual digits out loud. For 10, we'll say ''one-zero''. For 110, we'll say ''one-one-zero''.

Step 1 is to add your binary numbers according to the binary rules for addition

After recalling your binary numbers addition rules, you can now go ahead and add your binary numbers following the aforementioned rules. You add binary numbers just like you add other numbers, but keep in mind the rules of binary addition.

You go from right to left. So, adding 101 and 110, you begin on the right side and add the last digit of both numbers together (1 + 0). This equals 1. You write this digit down. This is the last digit, the end of your answer.

binary addition

You then move on and add up the digits to the left (0 + 1). This also equals 1. You write this to the left of the last digit of your answer.

binary addition

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