Bit operations: represent independent flags

A small local format stores three independent flags: read, write and execute. A single integer can carry all three, but each bit must have a declared meaning. Follow the numeric and binary forms together before using masks in a larger algorithm.

An integer's binary digits can represent independent on/off states. A mask selects the bits an operation cares about. This is useful for flags, compact subsets, and some counting techniques; clarity still matters more than a clever-looking expression.

READ = 1 << 0
WRITE = 1 << 1
EXECUTE = 1 << 2

permissions = READ | WRITE
print(bool(permissions & READ))     # True
print(bool(permissions & EXECUTE))  # False
permissions &= ~WRITE
print(permissions == READ)         # True

| enables bits, & selects common bits, ^ toggles differing bits, ~ inverts, and shifts move bit positions. These operators differ from the Boolean and/or operators. The small integers above are a representation example, not a complete authorization system.

Recognize the assumptions

x ^ x == 0 and x ^ 0 == x, so XOR can cancel paired integer values. It only isolates one unpaired value when the input guarantees the required multiplicities. It does not recover arbitrary missing or repeated values from any dataset.

For n flags, 0 .. (1 << n) - 1 enumerates 2ⁿ subsets. The representation is compact, but enumeration is still exponential. Python integers have arbitrary precision; fixed-width reasoning such as overflow and unsigned shifts does not transfer unchanged from other languages.

Check: READ|WRITE is binary 011; removing WRITE leaves 001; testing EXECUTE yields zero. If zero is a valid stored value, avoid treating it as “missing” through a truthiness check.

Translate the bit expression back into flags

This is a representation exercise. Real authorization also needs identity, resource scope and an enforcement point. An integer called permissions does not supply those decisions.