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Encoders, converters & dev utilities
Decimal to Binary Converter — with Step-by-Step Working
Convert a decimal number like 10 to binary and see the remainder ladder, not just the answer. The method is repeated division by 2: divide, record the remainder (0 or 1), then read the remainders bottom-to-top. Worked example: 10 ÷ 2 = 5 r0, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1 → reading upward gives 1010₂. Cross-checking with place values confirms it: 8 + 2 = 10. A value like 255 gives 11111111₂ (a full byte of ones). The step ladder is the educational payload an answer box skips. This tool shows all four bases at once, uses BigInt for large inputs, and runs 100% in your browser. Free, no login.
Decimal → binary = repeatedly divide by 2, collect each remainder, then read the remainders bottom-to-top
- Byte-exact worked example: 10 → 10÷2=5 r0, 5÷2=2 r1, 2÷2=1 r0, 1÷2=0 r1 → 1010₂
- Cross-check by place value: 1010₂ = 8 + 2 = 10₁₀ ✓
- 255₁₀ → 11111111₂ (a full byte of ones = 2⁸ − 1); also FF₁₆
- Large inputs use BigInt (no float error); runs 100% client-side
Frequently asked questions
How do I convert decimal to binary?
Divide the number by 2 over and over, writing down the remainder each time, until you reach 0. Then read the remainders from the last one back up to the first. For 10: 10÷2 = 5 remainder 0, 5÷2 = 2 remainder 1, 2÷2 = 1 remainder 0, 1÷2 = 0 remainder 1. Reading the remainders bottom-to-top gives 1010. The tool renders this whole ladder plus the hex and octal forms.
What is 255 in binary?
255 in binary is 11111111 — eight ones. That is because 255 is 2⁸ − 1, the largest value that fits in one unsigned byte, so every bit is set. In hexadecimal the same value is FF. This is why you often see 255 (or #FF) as the maximum for a color channel: it is a full 8-bit byte.
How do I check my decimal-to-binary answer?
Convert back using place values. Give each bit a value that doubles from the right (1, 2, 4, 8…) and add the values where the bit is 1. For 1010 that is 8 + 2 = 10, matching the input, so the conversion is correct. Doing the round-trip is the quickest way to catch a dropped or extra bit.