Electronic – Given 4 inputs (A,B,C,D) how can I design a circuit that counts the number of 1s

A half-adder is used for the first bit since there is no carry-in. For the second and subsequent bits, you need full adders.

This is a simple job for a microcontroller. Spehro correctly points out that it can be accomplished with a simple lookup. If you can tolerate lower speed then counting the bits in a loop will do it too, but will take less code space.

Another way is to do this in analog. Put a 100 kΩ resistor in series with each digital output, then feed that into a comparator. If 4 out of 8 are high, then you get 0.50 of the supply voltage. If 3 out of 8 are high, then you get 0.38 of the supply voltage. Set the comparator threshold to 0.44 of the supply and it will distinguish between 4 or more, and 3 or less.