Convert Decimal to Binary
Change any standard decimal number into binary. Just type your base 10 number below to get the base 2 binary value.
Decimal to binary converter
Quick Reference
Decimal to Binary Conversion Chart
Here is a quick reference table showing common decimal numbers in binary.
| Decimal | Calculation / Division by 2 | Binary |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 = 1×2¹ + 0×2⁰ | 10 |
| 3 | 3 = 1×2¹ + 1×2⁰ | 11 |
| 4 | 4 = 1×2² | 100 |
| 5 | 4 + 1 | 101 |
| 6 | 4 + 2 | 110 |
| 7 | 4 + 2 + 1 | 111 |
| 8 | 8 = 1×2³ | 1000 |
| 10 | 8 + 2 | 1010 |
| 15 | 8 + 4 + 2 + 1 | 1111 |
| 16 | 16 = 1×2⁴ | 10000 |
| 25 | 16 + 8 + 1 | 11001 |
| 100 | 64 + 32 + 4 | 1100100 |
| 255 | 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 | 11111111 |
Step by Step
How to Convert Decimal to Binary
Converting a decimal number to binary is easy when you follow the right steps.
The Method
Decimal is a base 10 number system that uses the digits 0 through 9. Binary is a base 2 system using only 0 and 1. To do the conversion, you divide your starting number by 2 over and over. You keep track of the remainders to build your final answer.
Keep dividing the decimal number by 2 until the math leaves you with a zero.
Convert Base 10 to Binary Steps
Write the decimal number
Take the number you want to convert. Let us use 10 as our example.
Divide by 2 repeatedly
Divide the number by 2 and write down the remainder. Keep dividing the new answer by 2 until you reach zero. For 10, the math looks like this: 10 ÷ 2 = 5 r0, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1.
Read remainders from bottom to top
Write those remainders in reverse order. Reading them from the last to the first gives you 1010. You just figured out that 10 in binary is 1010.
Decimal vs Binary
Understanding Decimal and Binary
Decimal and binary are just different ways to count. Decimal is the base 10 system we use every day. It uses ten different numbers from 0 to 9. Binary is a base 2 system. It only uses two numbers, 0 and 1.
Computers and electronics run on binary because hardware reads simple on and off signals. When you want to translate between the two, you can use our decimal to binary converter. You might also hear people call this converting denary to binary. They mean the exact same thing.
Worked Examples
Sample Decimal to Binary Conversions
Here is how to convert some of the most popular numbers to binary.
2 in binary
Divide 2 by 2 to get 1 with a remainder of 0. Divide 1 by 2 to get 0 with a remainder of 1. Read it backward to get 10.
3 in binary
3 divided by 2 gives a remainder of 1. Divide again to get another 1. The binary of 3 is 11.
4 in binary
Keep dividing by 2 and tracking the remainders. The binary for 4 is 100.
5 in binary
Dividing 5 by 2 leaves a remainder of 1. Continue the math to find that 5 in binary is 101.
8 in binary
Divide 8 by 2 to get 4, divide that by 2 to get 2, and so on. The result for 8 in binary is 1000.
10 in binary
Follow the division steps. You will see that 10 in binary is exactly 1010.
15 in binary
Divide 15 by 2 repeatedly. The remainders give you 1111.
100 in binary
100 divided by 2 leaves 0. Keep going until you reach 0. The binary value of 100 is 1100100.
FAQ
Frequently Asked Questions
Everything you need to know about changing dec to bin.