Bitwise Calculator

What each operator does

AND sets a result bit only where both inputs have a 1 — useful for masking off bits you want to keep. OR sets a bit where either input has a 1 — useful for combining flags. XOR sets a bit where the inputs differ — used to toggle bits or compute a difference. NOT flips every bit. NAND, NOR and XNOR are simply AND, OR and XOR with the result inverted — NAND and NOR are "universal" gates that any digital circuit can be built from using only one of them.

Arithmetic vs logical shift, and what sign extension does

A left shift (<<) always fills the vacated low bits with 0. A right shift has two different meanings depending on whether you care about the sign: an arithmetic shift (>>) fills the vacated high bits with copies of the sign bit, so a negative number shifted right stays negative — this is sign extension, and it is what almost every language's >> operator does by default. A logical shift (>>>) always fills with 0 regardless of sign, treating the value as a plain bit pattern rather than a signed number. This tool's shift receipt shows exactly which bits were dropped and whether sign extension happened, which is the detail behind most shift bugs.

Why 1 << 32 gives four different answers in four languages

JavaScript's native shift and bitwise operators coerce both operands to a signed 32-bit integer first, so a shift count is taken modulo 32 — 1 << 32 is 1, not 4294967296. C and Java's behaviour for a shift count at or past the type's width is undefined or implementation-defined for a 32-bit int, and can differ by compiler. Python has arbitrary-precision integers and no fixed width at all, so 1 << 32 is genuinely 4294967296 there. This tool takes an explicit width — including "no width" for arbitrary precision — so the answer is always the one you actually asked for.

How bit flags and masks work in practice

A bitmask is a value used with AND to test or clear specific bits, or with OR to set them — permission flags, feature toggles and CPU status registers are all commonly packed this way, one bit per flag. Testing whether a flag is set is value AND mask compared against the mask itself; setting it is value OR mask; clearing it is value AND (NOT mask).

Why 64-bit masks break most web calculators

Every calculator built on JavaScript's native bitwise operators truncates to 32 bits before doing anything, so a 64-bit mask — the normal case for a hash, a UUID, or a file permission bitmap — silently loses its top half. This tool runs entirely on BigInt, so 64-bit (and arbitrary-precision) masks compute exactly.

Common use cases

• Checking or combining permission/feature flags packed into one integer
• Understanding a shift bug — what actually fell off the end, and whether it sign-extended
• Computing a 64-bit bitmask without the silent 32-bit truncation JS calculators have
• Learning the difference between a shift and a rotate
• Seeing AND/OR/XOR visually, bit by bit, rather than as an opaque result