ماشین‌حساب عملیات بیتی

(مستندات به انگلیسی)

What it does

The Bitwise Calculator performs exact, width-masked bit operations on 8 / 16 / 32 / 64-bit values. Enter operands in binary, octal, decimal or hex - each operand keeps its own base - and read the result in every base at once in the sticky result panel, which carries badges for the active operator and width (e.g. XOR · 8-bit) and a live bit grid highlighting exactly which bits are set. Supported operations: AND, OR, XOR, NOT (unary), SHL/SHR (logical shifts), and ROL/ROR (rotates that wrap within the chosen width). All math runs on bigint, so results are exact with no floating-point rounding. Everything stays in your browser.

Operator reference

Operator	Symbol	Inputs	What it does
AND	&	A and B	1 where both operands have a 1 - masks and extracts bits
OR	|	A and B	1 where either operand has a 1 - sets and combines bits
XOR	^	A and B	1 where the operands differ - toggles bits
NOT	~	A only	Flips every bit within the chosen width (operand B is ignored)
SHL	<<	A, count B	Shifts A left by B; zeros enter from the right, bits pushed past the width are masked away
SHR	>>	A, count B	Logical shift right by B; zeros enter from the left
ROL	⟲	A, count B	Rotates left by B mod width; bits leaving the top re-enter at the bottom
ROR	⟳	A, count B	Rotates right by B mod width; bits leaving the bottom re-enter at the top

How to use it

1. The tool opens on a live sample - XOR of hex CA and 35 at 8-bit - so there is a computed result from the first paint. Edit either operand and the panel updates instantly.
2. Pick a width (8/16/32/64-bit) from the toolbar - this masks every value and result.
3. Choose an operation from the operator row (AND through ROR). Selecting NOT disables operand B.
4. Type Operand A (and Operand B for binary ops; for shifts and rotates B is the count). The BIN/OCT/DEC/HEX switch above each operand sets its base - prefixes like 0x / 0b / 0o are stripped automatically.
5. Read the result panel: Decimal, Hex, Octal and Binary lines plus the bit grid (MSB left, LSB right, highlighted bits are set). Copy result copies all four lines; Copy share link encodes the whole calculation in the URL.
6. Sample restores the built-in example; Clear empties both operands.

Examples

Every value below is the tool’s real output for the given input.

XOR two hex bytes (8-bit) - the default sample

width: 8-bit   op: XOR
A (hex): CA  → 1100 1010
B (hex): 35  → 0011 0101
result: dec 255 · hex 0xff · oct 0o377 · bin 1111 1111  (every bit set)

Mask with AND (32-bit)

A (hex): DEADBEEF   B (hex): 0000FFFF
result: dec 48879 · hex 0x0000beef · bin 0000 0000 0000 0000 1011 1110 1110 1111

NOT and shifts (8-bit)

op: NOT   A (hex): 0F, B: -        → dec 240 · hex 0xf0 · bin 1111 0000
op: SHL   A (hex): 01, B (dec): 4  → dec 16  · hex 0x10 · bin 0001 0000
op: SHR   A (hex): 08, B (dec): 1  → dec 4   · hex 0x04 · bin 0000 0100

Rotates wrap within the width (8-bit)

op: ROL   A (hex): 80, B (dec): 1  → dec 1   · hex 0x01 · bin 0000 0001
  (1000 0000 rotated left by 1: the top bit wraps around to bit 0)
op: ROR   A (hex): 01, B (dec): 1  → dec 128 · hex 0x80 · bin 1000 0000
  (0000 0001 rotated right by 1: bit 0 wraps around to the top)

Negative operands are normalized (8-bit)

A (dec): -1   op: AND   B (dec): 1
result: dec 1 · hex 0x01 · bin 0000 0001
  (-1 becomes 1111 1111, the 8-bit two's-complement pattern, before the op)

Good to know

• Two’s-complement masking: every value is normalized to the unsigned width-bit pattern before the op, and the result is masked back - so NOT 0x0F in 8-bit is 0xf0, never a giant negative number, and -1 in 8-bit behaves as 0xff.
• Shifts drop the overflow: 0xFF << 1 in 8-bit is 0xfe - the bit pushed past the width is gone, exactly like native fixed-width integers.
• Rotates wrap: ROL/ROR rotate by count mod width, so a rotate by the width itself is a no-op.
• Shareable: operands, bases, op and width are all encoded in the URL - open the link and the exact calculation is restored.
• Private: all calculation is local - nothing is sent anywhere.
• Related tools: Number Base Converter, JSON Formatter, Cron Expression Explainer.