Binary Calculator
Perform arithmetic operations on binary numbers and convert between binary and decimal values.
Binary arithmetic
Binary result:
Decimal result:
Hexadecimal result:
Convert binary to decimal
Decimal:
Convert decimal to binary
Binary:
How binary (base-2) numbers work
Binary uses only two digits, 0 and 1, with each position representing a power of 2 (1, 2, 4, 8, 16...) instead of the powers of 10 used in the decimal system. This calculator converts each binary input to decimal internally, performs the requested arithmetic, then converts the result back to binary (and hex) for display.
Frequently asked questions
Why does computing use binary instead of decimal? Digital circuits are built from transistors that are naturally either "on" or "off" — two states map directly onto the two binary digits, making binary the fundamental number system for how computers store and process all data.
How do I read a binary number like 1010? Each digit represents a power of 2 from right to left: 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10 in decimal.
What happens with binary division here? Division is performed on the decimal equivalents and rounded down to a whole number (integer division), since fractional binary results aren't handled by this calculator.