What is 10 in Binary? - How-to & Steps

Instructor: Yuanxin (Amy) Yang Alcocer

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

The number ten in decimal form, 10, is way different than the number ten in binary form, 1010. Learn the steps you need to take for you to write the number ten in binary in this lesson.

The Steps

Binary numbers are numbers written using only 0s and 1s. This can be confusing especially when you are talking about the number ten, 10, in decimal form. A big distinction between decimal numbers and binary numbers is that our decimal numbers is a base 10 numbering system while the binary numbers is a base 2 numbering system. The base tells you how many different numbers you can use to represent your numbers. We are used to the base 10 system; we count 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. That's 10 different numbers we use to count with. In the binary system, we have 0 and 1, just 2 numbers to count with.

Knowing this, we can now go ahead and follow these steps to turn our decimal ten into a binary ten.

Step 1: Start counting in binary.

To find what the number ten in binary is, we first start counting in binary. To count in binary, you start with 0, then you go to 1. Then you add another digit, like you do in decimal counting when you go from 9 to 10. You add another digit, so you have two digits now. So, in binary, you go from 1 to 10 since 1 is your last counting number. In decimal numbers, you go from 9 to 10 since 9 is your last number you can use when counting. Every time you reach the last counting number, you add another digit to your number.

So, counting in binary, you count like this:

0
1
10
11
100
101
110
111

Step 2: Keep counting until you reach ten.

In the last step, you just keep counting until you reach the number ten. When you've reached the number ten, you've found what it is as a binary number. To help you, you can have two columns, one for your binary counting and another for your decimal counting so you can see which one equals which number, like this:

Binary Decimal
0 0
1 1
10 2
11 3
100 4
101 5
110 6
111 7
1000 8
1001 9
1010 10

The Solution

When you are done counting, you'll see that the number 10 as a decimal number is 1010 as a binary number. Your answer is 1010.

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