Binary One Counter

Given a positive integer n, write a function that determines the count of active bits (bits set to 1) present in its binary representation. This count is commonly referred to as the population count or binary weight of the number.

For instance, the number 13 is represented in binary as 1101, which contains three active bits. Your task is to efficiently compute this count for any valid input within the specified constraints.

This problem explores fundamental bit manipulation techniques that form the foundation of many low-level programming concepts and optimizations used in systems programming, cryptography, and hardware design.