Set Bits Counter

Problem

Three small functions on an unsigned 32-bit value, no library calls, no lookup tables unless you build them yourself:

1. popcount(x) — number of bits set to 1.
2. swapNibbles(b) — for a byte, exchange the high and low 4 bits.
3. isPowerOfTwo(x) — true if exactly one bit is set (0 is not a power of two).

This is the first screen for embedded roles. I care less about the answer than about whether you reach for the bit tricks naturally.

Examples

Example 1 — popcount(0b1011_0001) = 4, popcount(0) = 0, popcount(0xFFFFFFFF) = 32.

Example 2 — swapNibbles(0xAB) = 0xBA, swapNibbles(0x0F) = 0xF0. isPowerOfTwo(64) = true, isPowerOfTwo(96) = false, isPowerOfTwo(0) = false.

Constraints

• Inputs are unsigned 32-bit (or 8-bit for the nibble swap). In C, use uint32_t / uint8_t and mask results.
• popcount should be O(number of set bits) per the classic x &= x - 1 trick; the naive 32-iteration loop is accepted as a warm-up.
• No __builtin_popcount; but tell me it exists and when you would use it.

What they look for

x & (x - 1) clears the lowest set bit, which gives both popcount and isPowerOfTwo (x && !(x & (x - 1))). Shifts and masks for the nibble swap, with awareness of integer promotion in C ((b << 4) becomes an int, so mask with 0xFF). Follow-ups go to reversing bits, counting trailing zeros, and the parallel-prefix popcount used by compilers.