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Encoders, converters & dev utilities
Binary to Decimal Converter — with Step-by-Step Working
Convert a binary number like 1010 to decimal and see every step, not just the answer. In positional notation each bit is worth a power of two, doubling from right to left (…8, 4, 2, 1), so the decimal value is the sum of the place values wherever there is a 1. Worked example: 1010₂ = 1·8 + 0·4 + 1·2 + 0·1 = 10₁₀. A byte of all ones, 11111111₂, is 128+64+32+16+8+4+2+1 = 255₁₀. The step-by-step derivation is the part an answer box skips — and the part a student needs. This tool shows all four bases at once, handles big values with BigInt, and runs 100% in your browser. Free, no login.
Binary → decimal = Σ (bit × 2^position), counting positions from 0 on the right (positional notation)
- Byte-exact worked example: 1010₂ = 1·8 + 0·4 + 1·2 + 0·1 = 10₁₀
- All-ones byte: 11111111₂ = 128+64+32+16+8+4+2+1 = 255₁₀
- Cross-check: 1010₂ = 10₁₀ = A₁₆ = 12₈ (all four bases shown at once)
- Large inputs use BigInt (no float rounding error); runs 100% client-side
Frequently asked questions
How do I convert binary to decimal?
Give each bit a place value that doubles from right to left — 1, 2, 4, 8, 16, and so on — then add the place values wherever the bit is 1. For 1010: the bits (left to right) sit in the 8, 4, 2, 1 columns, and the 1s are in the 8 and 2 columns, so 8 + 2 = 10. This tool shows that full working, not just the final number, and also gives the hex and octal forms.
What is 11111111 in binary as a decimal?
An 8-bit value of all ones is 255. Add the place values of all eight bits: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. That is the largest value an unsigned byte can hold (2⁸ − 1). Note that if the same 11111111 is interpreted as a signed 8-bit two's-complement number instead, it means −1, not 255 — the bits are identical, only the interpretation differs.
Why show the steps instead of just the answer?
Because the derivation is the learning. Anyone can be told 1010 is 10, but seeing 1·8 + 0·4 + 1·2 + 0·1 makes the positional system click and lets you convert the next number yourself. It also catches mistakes: if your hand calculation disagrees with a step, you can see exactly which place value you misread.