Bit Mask Calculator

Bit masks are used to store flags, permissions, packed data, and low-level state.

Use the result as a learning aid. For classwork, still show the formula and intermediate reasoning so the final answer is not just a black-box number.

A bit mask is a binary pattern used to inspect or change selected bit positions in an integer. A 1 in the mask marks a position affected by the operation; a 0 usually leaves that position unchanged or excludes it. AND keeps a bit only when both value and mask contain 1. OR sets every masked bit to 1. XOR toggles every masked bit. Clearing uses value AND NOT mask.

For example, decimal 13 is binary 1101 and decimal 10 is 1010. Their AND result is 1000₂ = 8 because only the highest shown bit is 1 in both values. Their OR result is 1111₂ = 15, while XOR gives 0111₂ = 7. These operations are widely used for flags, permissions, packed fields, hardware registers, and low-level protocols.

JavaScript bitwise operators work on signed 32-bit integer representations. That implementation detail matters for large values and for how the highest bit affects the displayed signed decimal result.

To build a mask from bit positions, remember that zero-based bit k has decimal value 2^k. Bit 0 is 1, bit 1 is 2, bit 2 is 4, bit 3 is 8, and so on. Combining positions uses OR: a mask for bits 0 and 3 is 0001₂ | 1000₂ = 1001₂ = 9.

Testing a flag commonly uses (value & mask) !== 0. Clearing a flag uses AND with the complemented mask, while toggling with XOR is reversible. These patterns let one integer store many independent yes/no settings compactly, but the chosen bit numbering and integer width should be documented so different systems interpret the mask consistently.