Count One Bits

What Is Hamming Weight / Population Count?

The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet. For a binary string, the **Hamming weight** is simply the total number of 1 bits in the value. In computer science, this calculation is commonly referred to as the **population count**, **popcount**, or **sideways sum**.

How to Count One Bits

To count the number of 1 bits manually, align the binary number and count each digit that contains a 1.

Example:

• Binary: 11001100 has **4** active bits (ones).
• Binary: 10101010 has **4** active bits (ones).
• Binary: 11110000 has **4** active bits (ones).
• Binary: 11111111 has **8** active bits (ones).

Efficiency & Algorithms

While counting ones by checking each bit sequentially is simple, processors use highly efficient, optimized methods to count bits in parallel:

1. Brian Kernighan’s Algorithm: Flips the least significant set bit using x = x & (x - 1) in a loop. The loop runs exactly as many times as there are set bits.
2. Popcount Instructions: Modern CPUs support hardware-level instructions (like Intel's POPCNT or ARM's CNT) that count all ones in a single clock cycle.