Binary Calculator
Perform binary arithmetic (add, subtract, multiply, divide) and convert between binary, decimal and hexadecimal.
How to use the Binary Calculator
- Enter your inputs into the Binary Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The base conversion mechanics
Decimal to binary: repeated division by 2; collect remainders bottom-to-top. Binary to decimal: multiply each bit by 2^position, sum.
Binary is base-2: each digit position represents a power of 2 (1, 2, 4, 8, 16, ...). Hex is base-16, often used as a compact representation of binary (each hex digit = 4 binary bits).
Worked example
Decimal 156 to binary: 156 = 128 + 16 + 8 + 4 = 10011100₂. Same number in hex: 9C. Binary addition: 1011 + 110 = 10001₂ (= 17 decimal).
Frequently asked questions
Why is binary used in computers?
Electronic circuits naturally have two states (on/off). Binary maps cleanly onto these states — every digital computation is ultimately binary arithmetic at the hardware level.
How does binary handle negative numbers?
Most modern systems use two's complement: invert all bits and add 1. So −5 in 8-bit two's complement is 11111011. This makes binary subtraction the same as adding the negative.
How big a number fits in N bits?
Unsigned N bits hold 0 to 2^N − 1. Signed N bits hold −2^(N−1) to 2^(N−1) − 1. 8 bits: 0–255 unsigned, −128 to 127 signed.