C Academy · Lesson

Practical Bit Tricks

Common techniques.

Lesson 4 of 413 steps

Practical Bit Tricks is a free C Academy lesson on CoddyKit. This is lesson 4 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the C Academy learning path, and your progress syncs across the web and the CoddyKit app. The C Academy course includes 4 lessons in total.

Useful Bit Tricks

Once you understand bitwise operators, a set of compact tricks becomes available. They are fast and appear often in real code.

Let us walk through the most common ones.

#include <stdio.h>

int main(void) {
    unsigned x = 6;
    printf("x & 1 = %u (odd if 1)\n", x & 1);
    return 0;
}

Even or Odd

The lowest bit tells parity. x & 1 is 1 for odd numbers and 0 for even numbers.

#include <stdio.h>

int main(void) {
    for (unsigned x = 0; x < 5; x++) {
        printf("%u is %s\n", x, (x & 1) ? "odd" : "even");
    }
    return 0;
}

Power of Two Check

A positive number is a power of two if it has exactly one bit set. The expression x & (x - 1) is 0 only in that case.

#include <stdio.h>

int is_pow2(unsigned x) {
    return x != 0 && (x & (x - 1)) == 0;
}

int main(void) {
    printf("%d %d %d\n", is_pow2(16), is_pow2(18), is_pow2(1));
    return 0;
}

Clear the Lowest Set Bit

x & (x - 1) clears the lowest set bit. This is the basis of the fast set-bit count.

#include <stdio.h>

int main(void) {
    unsigned x = 0b10110;
    printf("before: %u\n", x);
    printf("after:  %u\n", x & (x - 1));
    return 0;
}

Isolate the Lowest Set Bit

x & (-x) isolates the lowest set bit, leaving only that single bit on.

This relies on two's complement representation.

#include <stdio.h>

int main(void) {
    unsigned x = 0b10110;
    printf("lowest set bit = %u\n", x & (-x));
    return 0;
}

Counting Set Bits

Repeatedly clearing the lowest set bit counts how many bits are set, in as many steps as there are set bits.

#include <stdio.h>

int popcount(unsigned x) {
    int n = 0;
    while (x) { x &= (x - 1); n++; }
    return n;
}

int main(void) {
    printf("%d\n", popcount(255));
    printf("%d\n", popcount(0b1010));
    return 0;
}

Swapping Without a Temp

The XOR swap exchanges two integers using no extra storage.

#include <stdio.h>

int main(void) {
    int a = 3, b = 8;
    a ^= b; b ^= a; a ^= b;
    printf("a=%d b=%d\n", a, b);
    return 0;
}

Rounding Up to Power of Two

You can round an unsigned value up to the next power of two by smearing the highest bit downward, then adding 1.

#include <stdio.h>

unsigned next_pow2(unsigned v) {
    v--;
    v |= v >> 1; v |= v >> 2; v |= v >> 4;
    v |= v >> 8; v |= v >> 16;
    return v + 1;
}

int main(void) {
    printf("%u\n", next_pow2(17));
    printf("%u\n", next_pow2(100));
    return 0;
}

Checking if Bits Differ

Two values have different bits exactly where a ^ b has set bits. Counting those gives the Hamming distance.

#include <stdio.h>

int main(void) {
    unsigned a = 0b1101, b = 0b1011;
    unsigned diff = a ^ b;
    int count = 0;
    while (diff) { diff &= diff - 1; count++; }
    printf("hamming distance = %d\n", count);
    return 0;
}

Absolute Value Without Branch

Using the sign bit, you can compute an absolute value without an if. The mask is all ones for negatives, all zeros for non-negatives.

#include <stdio.h>

int main(void) {
    int x = -42;
    int mask = x >> 31;
    int abs = (x + mask) ^ mask;
    printf("abs = %d\n", abs);
    return 0;
}

Setting a Bit by Index

Combine shifting and OR to set an arbitrary bit position computed at runtime.

#include <stdio.h>

int main(void) {
    unsigned v = 0;
    int positions[] = {1, 3, 5};
    for (int i = 0; i < 3; i++) {
        v |= (1u << positions[i]);
    }
    printf("v = %u\n", v);
    return 0;
}

Quick Check

Test your knowledge of bit tricks.

Answer it in the interactive lesson

Recap

You learned practical bit tricks:

x & 1 tests odd/even.
x & (x - 1) clears the lowest set bit and detects powers of two.
x & (-x) isolates the lowest set bit.
Popcount, XOR swap, Hamming distance, and branchless absolute value.

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Frequently Asked Questions

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