Ken Shirriff writes:
How can you count bits in hardware? In this article, I reverse-engineer the circuit used by the ARM1 processor to count the number of set bits in a 16-bit field, showing how individual transistors form multiplexers, which are combined into adders, and finally form the bit counter. The ARM1 is the ancestor of the processor in most cell phones, so you may have a descendent of this circuit in your pocket.
More details at Ken Shirriff’s blog.