Solve AND, OR, XOR, NOT, and shifts. Enter decimal, binary, octal, or hexadecimal values easily. View synchronized outputs, bit counts, masks, and practical examples.
AND: R = A & B
OR: R = A | B
XOR: R = A ^ B
NAND: R = ~(A & B) & Mask
NOR: R = ~(A | B) & Mask
XNOR: R = ~(A ^ B) & Mask
NOT: R = ~A & Mask
Left Shift: R = (A << n) & Mask
Logical Right Shift: R = (A >> n) & Mask
Arithmetic Right Shift: Signed A is shifted right, then limited by the selected width.
Rotate Left: R = ((A << n) | (A >> (w - n))) & Mask
Rotate Right: R = ((A >> n) | (A << (w - n))) & Mask
Mask: Mask = (2w - 1), where w is the chosen bit width.
| Input Base | A | B / Count | Width | Operation | Result |
|---|---|---|---|---|---|
| Decimal | 29 | 15 | 8 | AND | 13 |
| Binary | 11101 | 01111 | 8 | XOR | 10010 |
| Hexadecimal | F0 | 0F | 8 | OR | FF |
| Decimal | 9 | 2 | 8 | Left Shift | 36 |
| Decimal | 177 | 3 | 8 | Rotate Right | 246 |
Bitwise math works at the level of individual bits. That makes it essential for binary logic, masks, flags, permissions, checksum routines, device control, and low-level optimization. A bitwise operation calculator removes slow manual conversions. It lets you test decimal, binary, octal, and hexadecimal values from one place. You can inspect fixed-width outputs immediately. That matters when one wrong bit changes an entire result.
AND keeps a bit only when both inputs contain one. OR sets a bit when either input contains one. XOR sets a bit when the inputs differ. NOT flips every bit inside the chosen width. Left shift moves bits toward higher positions. Right shift moves bits toward lower positions. Rotate operations wrap moved bits around the edge. These rules power masking, toggling, clearing, packing, and extracting data.
Bit width controls overflow, truncation, and sign interpretation. An 8-bit result is different from a 16-bit result, even when the starting value looks identical. Width also defines the mask used during normalization. Signed mode interprets the highest bit as a sign bit. Unsigned mode treats every bit as magnitude. This calculator shows both views, so you can compare stored patterns and human-readable values without guessing.
Students use bitwise tools to understand binary arithmetic and truth behavior. Programmers use them to encode state, merge flags, test permissions, and accelerate compact calculations. Network engineers read masks and flags. Embedded developers control registers. Security analysts inspect packed values. The calculator is also useful during interviews because it explains how each operation changes the underlying bit pattern. That makes learning faster and debugging cleaner.
Use this page when you need reliable conversion, fast comparison, and repeatable results. Enter values, choose the number base, set the width, select an operation, and review synchronized outputs. Export the final table for reports, notes, or homework. With clear formats and example rows, the calculator turns abstract bit logic into something practical, readable, and easy to verify. It also helps compare manual calculations with machine-style representations before writing code or solving complex exam questions.
It applies logic directly to the bits of one or two values. You can test AND, OR, XOR, NOT, shifts, and rotates while comparing decimal, binary, octal, and hexadecimal outputs together.
Bit width controls masking, overflow, and the visible number of bits. The same value can produce different results under 8-bit, 16-bit, or 32-bit limits because higher bits may be truncated.
Unsigned view treats every bit as magnitude. Signed view treats the highest bit as the sign bit. Both views can represent the same stored pattern, but the decimal meaning changes.
XOR is useful when you want bits set only where inputs differ. It is common in toggling flags, parity checks, error detection ideas, and simple low-level comparisons.
A shift moves bits and usually fills new positions with zeros. A rotate wraps the bits that leave one side back to the opposite side inside the chosen width.
Yes. Select the correct input base first. Then enter the digits in that base. The calculator will normalize the value to the chosen width and show synchronized outputs in all common formats.
Lower widths apply a smaller mask. Bits outside that width are discarded. This changes stored patterns, signed interpretation, and final results for complements, shifts, rotates, and inverse operations.
They are used in flags, permission systems, register control, packet parsing, image processing, compact storage, checksums, embedded systems, and programming tasks where binary precision matters.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.