The Binary Calculator adds, subtracts, multiplies and divides binary numbers and converts between binary and decimal.
10101010 + 11001100 = 101110110
| Result | 101110110 |
| In decimal | 170 + 204 = 374 |
| Decimal value | 170 |
| Binary value | 10101010 |
Binary is a base-2 number system that uses only the digits 0 and 1. Each place is worth twice the place to its right: 1, 2, 4, 8, 16, … Computers use binary because electronic circuits have two stable states, on and off.
Multiply each digit by its place value and add. 10101010 = 128 + 32 + 8 + 2 = 170. To go from decimal to binary, divide by 2 repeatedly and read the remainders from bottom to top: 170 → 85 r0 → 42 r1 → 21 r0 → 10 r1 → 5 r0 → 2 r1 → 1 r0 → 0 r1, giving 10101010.
Addition follows 0+0 = 0, 0+1 = 1, 1+1 = 10 (write 0, carry 1). Subtraction borrows 2 instead of 10. Multiplication is shifting and adding; division works like long division. Example: 10101010 + 11001100 = 101110110 (170 + 204 = 374).
Computers usually store negative integers in two's complement: invert all bits and add 1. In 8 bits, −1 is 11111111. This calculator works with ordinary signed binary numbers of any length.
What is a bit and a byte? A bit is one binary digit; a byte is 8 bits.
How high can 8 bits count? 0 to 255.
Is division exact? The calculator shows the whole-number quotient and the remainder.