Binary Calculator
Binary arithmetic and binary ↔ decimal conversion
Result
In decimal
- 45 + 11 = 56
- 1Choose a taskCalculate or convert
- 2Type your numbersOnly 0s and 1s for binary
- 3See the answerIn binary, decimal, hex and octal
How does binary work?
Binary is base 2: each place is worth twice the one to its right. A 1 means that place value counts; a 0 means it doesn't.
101101₂ = 32 + 8 + 4 + 1 = 45
Addition: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1)
Decimal → binary: divide by 2 repeatedly, read remainders upwards
Why computers use binary
Electronic circuits are most reliable with two states, on and off. Every number, letter and image in a computer is stored as patterns of 1s and 0s called bits; 8 bits make a byte.
AND, OR and XOR
These compare numbers bit by bit. AND gives 1 only where both bits are 1; OR gives 1 where either is 1; XOR gives 1 where exactly one is 1. They're used in programming for masks and flags.
Related calculators
Frequently asked questions
How do I convert binary to decimal?
Multiply each digit by its place value (1, 2, 4, 8, 16… from the right) and add them. 1011 = 8 + 0 + 2 + 1 = 11.
How do I convert decimal to binary?
Divide by 2 repeatedly and write down each remainder. Reading the remainders from the last to the first gives the binary number. 13 → 1101.
What is 1 + 1 in binary?
10. That's 2 in decimal: you write 0 and carry 1 to the next place.
Last reviewed: October 2026