Decimal to Binary Converter
Type a whole number to get it in binary, with the divide-by-two working you would do on paper.
1001 11002341569CWorking
| Divide | Quotient | Remainder |
|---|---|---|
| 156 ÷ 2 | 78 | 0 |
| 78 ÷ 2 | 39 | 0 |
| 39 ÷ 2 | 19 | 1 |
| 19 ÷ 2 | 9 | 1 |
| 9 ÷ 2 | 4 | 1 |
| 4 ÷ 2 | 2 | 0 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |
The method
Divide by 2 and write down the remainder. Keep dividing the quotient until it reaches 0. The remainders read from bottom to top are the binary number.
Place value: the idea behind every base
In any base, a digit’s worth depends on its column. Each column is worth the base times the column to its right. Tap a digit to change it and watch the total.
1×32 + 1×8 + 1×4 + 1×1 = 45 in decimal
Decimal is the same system with ten digits: 347 is 3×100 + 4×10 + 7×1. Nothing about base 10 is special apart from our ten fingers.
Decimal to binary table
| Decimal | Binary |
|---|---|
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 8 | 1000 |
| 10 | 1010 |
| 16 | 10000 |
| 32 | 100000 |
| 50 | 110010 |
| 64 | 1000000 |
| 100 | 1100100 |
| 127 | 1111111 |
| 128 | 10000000 |
| 255 | 11111111 |
| 1000 | 1111101000 |
Questions people ask
How do you convert decimal to binary?
Repeatedly divide by 2, noting each remainder (0 or 1), until the quotient is 0. Reading the remainders from last to first gives the answer. 13 → 6 r1 → 3 r0 → 1 r1 → 0 r1, so 13 = 1101.
How are negative numbers written in binary?
Computers use two’s complement: invert every bit of the positive number and add 1. −5 in 8 bits is 11111011. The table under the result shows 8, 16 and 32-bit forms.
What is 100 in binary?
100 in decimal is 1100100 in binary (64 + 32 + 4).