Design a clocked synchronous circuit with four inputs, N$3,$ N$2,$ N$1,$ and N$0$ that represent the integer N in the range $0-15.$ The circuit has a single output Z that is HIGH for exactly N clock ticks during any $16-$tick interval. Include a schematic in your answer.

$($Hints: use a free$-$running $4-$bit counter IC and combinational logic to decode the N bits. The ticks in which Z is HIGH should be spaced as evenly as possible. For example, every second tick when N $=8,$ every fourth when N $=4,$ and so on$.)$