12. A "population count" circuit counts the number of '1's in an input vector. Build a population count circuit for a 3-bit input vector. 13. Create a one-bit wide, 2-to-1 multiplexer. When sel=0, choose a. When sel=1, choose b. 14. Create a 100-bit wide, 2-to-1 multiplexer. When sel=0, choose a. When sel=1, choose b. 15. Create a 16-bit wide, 9-to-1 multiplexer. sel=0 chooses a, sel=1 chooses b, etc. For the unused cases (sel=9 to 15), set all output bits to '1'. 16. HA Create a half adder. A half adder adds two bits (with no carry-in) and produces a sum and carry-out. 17. FA Create a full adder. A full adder adds three bits (including carry-in) and produces a sum and carry-out. 18. ADD4 18. BCDADD You are provided with a BCD (binary-coded decimal) one-digit adder named bcd_fadd that adds two BCD digits and carry-in, and produces a sum and carry-out. 19. Build a circuit to implement KMAP1 and KMAP2