Bitwise Calculator (Programmer Calculator)

Bit masks, flags, register values and hash functions are easier to reason about when you can see the bits. This programmer calculator applies AND, OR, XOR, NOT, NAND, NOR, XNOR, shifts, rotates and single-bit set/clear/toggle/test to 8-, 16-, 32- or 64-bit integers, and wraps addition, subtraction and multiplication the way fixed-width hardware does. Enter numbers in decimal, hex, binary or octal; every result is shown in all four, as signed and unsigned, with its population count and leading and trailing zeros.

How to use this tool

1. Enter A, in decimal (negative numbers become two's complement), 0x hex, 0b binary or 0o octal.
2. Choose the operation.
3. Enter B — a second operand, a shift or rotate amount, or a bit number counted from 0 at the right.
4. Pick the width; values must fit in it.
5. Read the result in hex, binary, decimal (unsigned and signed) and octal.

Formula

AND 1∧1 = 1 · OR 0∨0 = 0 · XOR 1⊕1 = 0 · NOT flips every bit · A << n = A × 2ⁿ mod 2ʷ · A >>> n = ⌊A ÷ 2ⁿ⌋

All arithmetic is exact (BigInt) and masked to the chosen width w. The arithmetic shift >> copies the sign bit into the vacated positions (the signed value is divided by 2ⁿ, rounding down); the logical shift >>> fills them with zeros. Rotates move bits that fall off one end back in at the other. Signed values use two's complement: a pattern with the top bit set means value − 2ʷ.

Example

A = 0b1100_1010 (0xCA, 202) AND B = 0x0F keeps only the low four bits: 0x0A = 0000 1010 = 10. With A = −16 in 8 bits (0xF0), an arithmetic shift right by 2 gives 0xFC = −4, while a logical shift gives 0x3C = 60.