Binary Calculator

Add column by column from the right: 0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 10 (write 0, carry 1) and 1 + 1 + 1 = 11 (write 1, carry 1). For example 101101 + 11011 = 1001000, which is 45 + 27 = 72 in decimal.

Subtract column by column with borrowing: 10 − 1 = 1 when you borrow from the next column. Computers usually subtract by adding the two's complement of B instead. This calculator shows the exact result, including negative results.

They compare the numbers bit by bit. AND gives 1 only where both bits are 1, OR gives 1 where at least one bit is 1, and XOR gives 1 where the bits are different. 1100 AND 1010 = 1000, OR = 1110, XOR = 0110.

A left shift by n moves every bit n places left and fills with zeros, which multiplies by 2^n (1011 << 3 = 1011000, 11 × 8 = 88). A right shift by n drops the lowest n bits, which divides by 2^n and rounds down.

NOT flips every bit, but a number has infinitely many leading zeros in theory. Choosing a width such as 8 bits fixes how many bits are flipped: NOT 00110101 in 8 bits is 11001010.

Binary long division works like decimal long division but each step is just 'does it fit: 0 or 1'. The calculator gives the whole-number quotient and the remainder, for example 1101 ÷ 11 = 100 remainder 1 (13 ÷ 3 = 4 r 1).