This binary calculator performs arithmetic and bitwise operations on binary numbers and shows the answer in binary, decimal and hexadecimal. It handles very large numbers exactly.
How binary works
Binary is base 2: each digit is 0 or 1, and each place is worth twice the one to its right (1, 2, 4, 8, 16 …). So 1011 = 8 + 0 + 2 + 1 = 11 in decimal.
Worked example
1011 (11) + 110 (6) = 10001, which is 17 in decimal and 11 in hex.
Frequently asked questions
What do AND, OR and XOR do?
They compare the numbers bit by bit. AND gives 1 only where both bits are 1; OR gives 1 where either is 1; XOR gives 1 where the bits differ. They are used in programming, networking and encryption.
How is division handled?
Binary division here gives a whole-number quotient and a remainder, like long division with integers.
Working in base 16 instead? Use the hex calculator.