What Are Bitwise Operations?

A bitwise operations calculator performs logic on the binary digits of integers. Every operation here works on 8-bit representations: AND, OR, XOR, NAND, and NOR compare the two operands bit by bit; NOT inverts all bits; and the shift operators move the pattern left or right. These are the exact primitives implemented by CPU instruction sets and used throughout low-level programming.

Two's Complement

This calculator interprets the 8-bit result as a signed two's complement value, so the range is −128 to 127. When the most significant bit is 1, the value is negative. That is why NOT 12 (00001100) gives 11110011, which reads as −13 — flipping all bits of x always yields −x − 1.

Where Bitwise Logic Is Used

Bit masking (AND) isolates flags inside a single byte, XOR powers checksums and light encryption, OR merges option flags, and shifts replace multiplication and division by powers of two. Networking uses bitwise AND for subnet masks, and graphics formats pack color channels with shifts and masks.