Binary to Decimal Converter
Convert binary to decimal by adding up place values, with every step shown, and see the number in octal and hex too.
In binary
10011100₂
156₁₀ = 10011100₂.
- Binary
- 10011100
- Octal
- 234
- Decimal
- 156
- Hex
- 9C
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How to convert binary to decimal
In binary each place is worth twice the place to its right: 1, 2, 4, 8, 16, 32, 64, 128 and so on, starting from the right. Multiply each bit by its place value and add. For 10011100:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
The 1s are in the 128, 16, 8 and 4 places, so 10011100 = 128 + 16 + 8 + 4 = 156.
Another way: double and add
Start with 0. For each bit from the left, double what you have and add the bit. For 10011100: 1, 2, 4, 9, 19, 39, 78, 156. This is handy for long numbers, because you never need the big place values.
Binary to hex in one step
Each hex digit is exactly 4 bits, so group the bits in fours from the right and convert each group: 1001 1100 → 9 and C, so 10011100 = 9C in hex. Groups of three give octal digits the same way: 10 011 100 → 234.
| Bits | Decimal | Hex | Bits | Decimal | Hex |
|---|---|---|---|---|---|
| 0000 | 0 | 0 | 1000 | 8 | 8 |
| 0001 | 1 | 1 | 1001 | 9 | 9 |
| 0010 | 2 | 2 | 1010 | 10 | A |
| 0011 | 3 | 3 | 1011 | 11 | B |
| 0100 | 4 | 4 | 1100 | 12 | C |
| 0101 | 5 | 5 | 1101 | 13 | D |
| 0110 | 6 | 6 | 1110 | 14 | E |
| 0111 | 7 | 7 | 1111 | 15 | F |
Questions
What is 1111 in decimal?
15: 8 + 4 + 2 + 1. In general, n ones in a row make 2n − 1, so 11111111 is 255.
How can I read binary quickly?
Learn the place values for one byte, 128, 64, 32, 16, 8, 4, 2, 1, and add the ones where there is a 1. With practice, 4-bit groups become instant: 1010 is 10 and 1111 is 15.
What does the little 2 in 1011₂ mean?
It is the base. 1011₂ is binary (eleven), while 1011₁₀ is the ordinary decimal number one thousand and eleven. Programmers often write 0b1011 instead.
Can I paste binary with spaces?
Yes. Spaces and underscores are ignored, so 1001 1100 and 1001_1100 both work, and so does a 0b in front.
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