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Math for Kids23 chapters | 325 lessons

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Instructor:
*Suzanne Rose*

Suzanne has taught all levels PK-graduate school and has a PhD in Instructional Systems Design. She currently teachers literacy courses to preservice and inservice teachers.

How would you like to learn to 'talk' to a computer? Computers use binary coding to work. In this lesson, you'll learn all about binary numbers, how to read them, and how we use them. Read on to learn 'computer talk!'

Our decimal number system is based on ten, sometimes called base ten. This means that in our number system, we represent amounts using ten numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When we need to write a larger number, we reuse the same numerals and make use of place value.

Place value means that each column, or place, in a number has a particular value. Each place to the left increases by a power of ten. Base ten seems simple and easy to us because we've used it a long time.

The **binary number system**, also called **base two**, works similarly to the base ten system. Since it is base two, we can only use two numerals: **0 and 1**. With base two, we also use place value: each place to the left increases in size by a factor of 2.

Here are the place values for the first five base two columns.

Using the chart that shows the place value for the first five columns in base two, you can convert base two numbers to base ten numbers. Let's do an example together.

You want to change the base two number 101 into a decimal number.

- To do this, start with the column on the far right, the 1 column. There is a 1 in that column. So you would multiply 1 x 1 = 1.
- Move to the next column to left, which is the 2 column. You have 0 in that column, so you would multiply 0 x 2 = 0.
- Then move to the next column to left, which is the 4 column. You have a 1 in that column, so you would multiply 1 x 4 = 4.
- Add the numbers you have gotten together to get the base ten number. 1 + 0 + 4 = 5. So, 101 in base two (binary) is the same as the number 5 in base ten (decimal).

Here are a few more examples of base two numbers changed into base ten numbers:

Aboriginal peoples in Australia used a base two counting system, so binary numbers are not new. African tribes used a binary system of high and low drum beats to send messages to people at a distance. In 1666, in a published article, Gottfried Leibniz explained how thought could be represented by patterns of numbers, which set the stage for the use of binary numbers in later machines.

Some early machines that were used to weave cloth used a wooden board punched with holes to help the machine make complex patterns in the cloth. These boards were actually a binary system of hole/no hole that was used to make the pattern. These early punched wooden cards actually inspired the first computers!

Today's computers still run on a binary number system. Computer programs use patterns of 0 and 1 to send instructions to the computer. Basically, the 0 turns off some switches in the computer and the 1 turns other switches on. The on and off patterns make the computer do many complex tasks.

The **binary number system**, also called **base two**, uses the numerals **0 and 1** in order to represent numbers. Each place column of the base two number corresponds to a power of two. Binary systems have been used throughout history for various things, such as Aboriginal Australian counting and African drum messages, and is currently used for complex computer programs.

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Math for Kids23 chapters | 325 lessons

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