Design a $3-$bit input and $1-$output circuit that can detect numbers that are divisible by $2,$ or divisible by $3,$ or divisible by both. For example, $6$ is divisible by $2$ and $3,$ so the output is $1.$ There should be a single output line, which would be $1$ if the condition is true, otherwise the output would be $0.$ Derive the truth table, derive the Boolean expression, minimize the Boolean expression. Draw the logic circuit. Implement the logic circuit using PLA programmable logic array.