Binary to Decimal Converter
Type a base-2 number and get its decimal value, with the place-value steps worked out for you.
Decimal
| Binary | Decimal | Hex | Octal |
|---|
Going the other way? Use the decimal to binary converter.
To convert binary to decimal, give each digit a place value starting at 1 on the right and doubling leftward, then add the values where a 1 appears. The number 1101 has 1s over 8 + 4 + 1, and that sum is 13. The converter shows this breakdown live.
How it works
Binary is a positional system just like decimal, but each place is worth twice its right-hand neighbor instead of ten times. From the right, the places count 1, 2, 4, 8, 16, and keep doubling. A digit of 1 means "include this place value", and a 0 means "skip it".
Worked example with 1101. Four digits, so four places worth 8, 4, 2, and 1 from left to right. The 1s sit over the 8, the 4, and the 1, while the 2 sits under a 0 and drops out. Add what remains: 8 + 4 + 1 = 13. That is the entire method, and it works unchanged on binary numbers of any length.
The converter also prints the same value in hex and octal, since those bases are the two common shorthands for binary, and it accepts a 0b prefix, spaces, or underscores in the input if you paste numbers formatted that way. Type 1101 above and watch the table walk through each bit's contribution.
Two quick sanity checks worth knowing. A binary number ending in 1 always converts to an odd decimal number, and n digits can never exceed one less than 2 to the n, so a five-digit binary number tops out at 31. If a hand conversion breaks either rule, a place value slipped somewhere. The full method, plus a faster doubling trick, lives in the binary to decimal guide.
Binary place values
| Power of 2 | Decimal | Binary |
|---|---|---|
| 2^7 | 128 | 10000000 |
| 2^6 | 64 | 1000000 |
| 2^5 | 32 | 100000 |
| 2^4 | 16 | 10000 |
| 2^3 | 8 | 1000 |
| 2^2 | 4 | 100 |
| 2^1 | 2 | 10 |
| 2^0 | 1 | 1 |
Each power of two is a 1 followed by that many zeros in binary, the same way powers of ten look in decimal.
FAQ
How do I convert binary to decimal?
Label each binary digit with a place value, starting at 1 on the right and doubling as you move left. Then add the place values wherever the digit is 1. For 1101, the switched-on places are worth 8 + 4 + 1, which adds up to 13.
What does the steps table under the result show?
It lists every digit of your binary number next to its place value and what it adds to the total. Bits set to 1 contribute their place value, bits set to 0 contribute nothing, and the note above the table spells out the final addition so you can follow the whole calculation.
Can it handle very large binary numbers?
Yes. The converter uses exact whole-number math, so results stay correct far beyond the point where ordinary calculators start rounding. Type a binary number hundreds of digits long and the decimal answer is still exact. The steps table appears for numbers up to 32 bits to stay readable.