Binary calculator
Convert between decimal and binary and do base-2 arithmetic. For step-by-step conversion, use the solver on the home page.
Binary calculation – Addition, Subtraction, Multiplication or Division
Result
Binary value:
+ =
Decimal value:
Convert Binary to Decimal
=
Convert Decimal to Binary
=
Binary in short
Binary is base 2: only 0 and 1. Each place is a power of 2 (2⁰, 2¹, 2², …).
Use this tool to convert and check base-2 numbers.
Conversion methods
- Decimal → Binary: divide by 2 repeatedly; read remainders from bottom to top.
- Binary → Decimal: add up each bit × 2ⁿ for its position.
- Check: convert the binary result back to decimal to verify.
Examples
19 in binary: 19÷2→9 R.1; 9÷2→4 R.1; 4÷2→2 R.0; 2÷2→1 R.0; 1÷2→0 R.1 → 10011₂.
10110₂ in decimal: 1×16 + 0×8 + 1×4 + 1×2 + 0×1 = 22.
Add: 1100₂ + 101₂ = 10001₂ (carry as in base 10).
Where binary turns up
- How computers represent data (on/off, 0/1).
- Colour codes, memory addresses and bit masks.
- Powers of 2: bytes, kilobytes and so on.
Quick reference
- Why binary? Two states (0/1) are easy to represent in electronics.
- Common slip: forgetting which power of 2 each position represents (2⁰, 2¹, 2², …).
- For the conversion method step by step, use the solver on the home page.