What do AND, OR and XOR do bit by bit?

AND sets a result bit to 1 only if both input bits are 1. OR sets it if either input bit is 1. XOR sets it if exactly one input bit is 1. NOT flips every bit of a single operand.

Why does the result depend on bit width?

NOT and negative numbers are width-dependent: inverting an 8-bit value flips 8 bits, but a 32-bit value flips 32. The width masks the result so it matches the register size you are modelling.

Can I mix decimal, hex and binary inputs?

Yes. Each operand is parsed independently: a plain number is decimal, a 0x prefix is hexadecimal, and a 0b prefix is binary. The result is then shown in all three bases.

What is a common use for XOR?

XOR is used in simple ciphers, checksums and parity, and the classic trick of swapping two variables without a temporary. XORing a value with itself yields zero, and with a key twice restores the original.

Is the calculation private?

Yes. All operations run locally with exact BigInt arithmetic, so values up to 64 bits are precise and nothing is sent over the network.

Bitwise Calculator — Gera Tools

A bitwise calculator applies Boolean logic to each pair of bits in two integers. These operations are the foundation of flags, bitmasks, permissions, checksums and low-level protocol work. This tool accepts decimal, hex or binary input and shows the result in all three bases.

How it works

Each operation compares the operands bit by bit:

AND (&) — result bit is 1 only when both input bits are 1. Used to mask/clear bits.
OR (|) — result bit is 1 when either input bit is 1. Used to set bits.
XOR (^) — result bit is 1 when the input bits differ. Used for toggling and parity.
NOT (~) — flips every bit of operand A.

Because NOT and signed values depend on register size, the result is masked to your chosen width with mask = (1 << width) - 1. So NOT of an 8-bit value inverts exactly 8 bits.

Example

With A = 0b1100 (12) and B = 0b1010 (10):

A AND B = 0b1000 = 8
A OR B = 0b1110 = 14
A XOR B = 0b0110 = 6
NOT A (8-bit) = 0b11110011 = 243

Notes

Common idioms: set bit n with x | (1 << n), clear it with x & ~(1 << n), toggle it with x ^ (1 << n), and test it with x & (1 << n). The width selector lets you reproduce the exact wraparound behaviour of a fixed-size register.