Binary calculator
Convert between decimal and binary, and run base-2 arithmetic. For a step-by-step breakdown of any conversion, use the solver on the home page.
Binary calculation – Addition, Subtraction, Multiplication or Division
Result
Binary value:
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Decimal value:
Convert Binary to Decimal
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Convert Decimal to Binary
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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: repeated division by 2, read remainders from bottom to top.
- Binary → Decimal: sum of bits × 2ⁿ according to position.
- Control: The binary result can be converted back to decimal.
Examples
27 in binary: 27÷2→13 R.1; 13÷2→6 R.1; 6÷2→3 R.0; 3÷2→1 R.1; 1÷2→0 R.1 → 11011₂.
1111₂ in decimal: 1×8 + 1×4 + 1×2 + 1×1 = 15.
Add: 1010₂ + 111₂ = 10001₂ (carry as in base 10).
Where binary is used
- How data is represented in circuits.
- Color coding, memory addresses, bit masks.
- Understanding powers of 2 (bytes, kilobytes, etc.).
Quick reference
- Why Binary? Two states (0/1) are reliable in electronics.
- Common errors: forgetting the positions (2⁰, 2¹, 2² …).
- To see the conversion method step by step, use the solver on the home page.