Binary to decimal converter
Enter a binary number and get its decimal value instantly, plus the other bases and the step-by-step working. Handles huge numbers, negatives and fractions.
Working for 1011012
Multiply each digit by its place value
- 1 × 2^51 × 32= 32
- 0 × 2^40 × 16= 0
- 1 × 2^31 × 8= 8
- 1 × 2^21 × 4= 4
- 0 × 2^10 × 2= 0
- 1 × 2^01 × 1= 1
Add them up: 45 in decimal.
How to convert binary to decimal
- Write the place value above each bit, starting with 1 on the right and doubling leftwards: 1, 2, 4, 8, 16, 32, 64, 128…
- Add up the place values that have a 1 under them. Ignore the 0s.
- For 1011: 8 + 0 + 2 + 1 = 11.
Binary is how hardware stores everything: bit flags, network masks, file permissions and machine code are all patterns of 1s and 0s. Decimal is the base people count in, so it is the usual starting or ending point when you need a value a human can check.
See place value move
Every bit is worth twice the bit to its right. Flip the switches and watch the decimal, hex and octal values rebuild.
32 + 8 + 4 + 1 = 45 · hex 2D · octal 55
Related conversions
Binary to octal · Binary to hex · Octal to decimal · Decimal to binary · Hex to decimal · any base 2–36 · signed (two's complement)
Questions people ask
How do you convert binary to decimal?
Write the place value above each bit, starting with 1 on the right and doubling leftwards: 1, 2, 4, 8, 16, 32, 64, 128… Add up the place values that have a 1 under them. Ignore the 0s. For 1011: 8 + 0 + 2 + 1 = 11.
What is 101101 in decimal?
101101 in binary (base 2) is 45 in decimal (base 10).
Does it handle negative numbers and fractions?
Yes. A leading minus sign is kept, and digits after a point are converted too. Some fractions that end in one base repeat forever in another (0.1 in decimal is 0.000110011… in binary), so the result is cut at 24 digits and marked as repeating.
Is there a size limit?
No practical one. The converter uses arbitrary-precision integers (JavaScript BigInt), so 64-bit, 128-bit and longer values convert exactly, without rounding.