Decimal to Binary Converter
Convert a decimal number to binary by dividing by 2 again and again, with every division shown, and see it in octal and hex too.
In binary
10011100₂
156₁₀ = 10011100₂.
- Binary
- 10011100
- Octal
- 234
- Decimal
- 156
- Hex
- 9C
Show me how
Why does this work?
All steps as text
Tip: press ← and → to move between steps, or click any step.
How to convert decimal to binary
Divide by 2 again and again, writing down each remainder, until the answer is 0. The remainders, read from the bottom up, are the binary digits. For 156:
- 156 ÷ 2 = 78, remainder 0
- 78 ÷ 2 = 39, remainder 0
- 39 ÷ 2 = 19, remainder 1
- 19 ÷ 2 = 9, remainder 1
- 9 ÷ 2 = 4, remainder 1
- 4 ÷ 2 = 2, remainder 0
- 2 ÷ 2 = 1, remainder 0
- 1 ÷ 2 = 0, remainder 1
Reading the remainders upwards gives 10011100, so 156 in binary is 10011100. Each division by 2 splits off the last binary digit, which is why the first remainder ends up last.
Another way: take away powers of 2
Find the biggest power of 2 that fits, take it away, and repeat. For 156: 128 fits, leaving 28; 16 fits, leaving 12; 8 fits, leaving 4; 4 fits, leaving 0. Write a 1 under 128, 16, 8 and 4 and a 0 under the other places:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 to 16 in binary
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 0 | 0 | 9 | 1001 |
| 1 | 1 | 10 | 1010 |
| 2 | 10 | 11 | 1011 |
| 3 | 11 | 12 | 1100 |
| 4 | 100 | 13 | 1101 |
| 5 | 101 | 14 | 1110 |
| 6 | 110 | 15 | 1111 |
| 7 | 111 | 16 | 10000 |
| 8 | 1000 | 255 | 11111111 |
Bits and bytes
Each binary digit is a bit. A byte is 8 bits, from 00000000 (0) to 11111111 (255), which is why so many computer settings stop at 255. 16 bits go up to 65,535, and 32 bits up to 4,294,967,295.
Questions
What is 10 in binary?
1010. 10 = 8 + 2, so there are 1s in the 8 and 2 places and 0s in the 4 and 1 places.
How do computers write negative numbers in binary?
Usually with two’s complement: write the positive number, flip every bit, and add 1. In 8 bits, 5 is 00000101, so −5 is 11111010 + 1 = 11111011. This converter works with whole numbers from 0 up.
How do I convert a decimal fraction like 0.625 to binary?
Multiply by 2 again and again and keep the whole-number parts: 0.625 × 2 = 1.25 (1), 0.25 × 2 = 0.5 (0), 0.5 × 2 = 1 (1). So 0.625 = 0.101 in binary. This converter handles whole numbers.
Why do computers use binary?
A computer stores everything with tiny switches that are either off or on. Two states fit two digits, 0 and 1, so binary is the natural way for a machine to count.
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