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Information Systems: Help and Review19 chapters | 387 lessons | 4 flashcard sets

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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.

**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:

- 0 + 0 = 0
- 0 + 1 = 1 or 1 + 0 = 1
- 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.

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.

Lastly, you add 1 + 1. This gives you 10. You write this in the front of your answer. Just like with addition, you write down your answer from right to left as you find the digits of your answer.

After adding everything up, your solution is 1011.

Now, just like with addition, you'll sometimes need to carry a digit over.

For example, say you now need to add 1011 + 111 together. You begin at the far right. You add the 1 + 1 together. Following the addition rules for binary numbers, you get 10. But since you aren't done adding your two numbers together, you need to carry, just like you would have to carry if you were adding 145 + 78. So you write down the 0 and you carry the 1.

Now, you need to add three 1s together. Well, you know that 1 + 1 = 10. 10 + 1, then is 11. You still aren't done adding the two numbers, so you'll have to carry again. You write down 1 and you carry the 1.

Continuing the addition and moving towards the left, you now need to add 0 + 1 + 1 (the carry). You know that 0 + 1 = 1. Then 1 + 1 = 10. You need to carry one more time. You write the 0 and carry the 1.

Now you can finish off by adding the remaining 1 with the 1 being carried over. You get 10. So you write down 10 at the very beginning of your answer. So your final answer is 10010.

A good thing to remember when working with your binary numbers is to not think of them as your regular counting numbers. Otherwise, you'll get confused when you add 1 + 1 and you get 10 instead of 2. Think of binary numbers as computer language where you only have 0 and 1.

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