Question 3: Design a combinational circuit with 4 inputs, A3, A2, A1, Ao; and three outputs, X, Y, Z. The inputs represent a binary number in the range [0..15), and the outputs represent characteristics of the numbers. Specifically, X should be true if the number is divisible by 3; Y should be true if the number is divisible by 4; and Z should be true if the number is divisible by 7. As an example, if the input is AAA,A,- 1100. this represents the number 12, which is divisible by 3 and 4 but not 7, so the output should be XYZ=110. Recall that 0 is divisible by any integer. (a) Implement the circuit with AND gates, OR gates, and NOT gates. inverted inputs are OK. You may use the k-map template provided for your design work. You may use inverted inputs on gates. (b) Implement the circuit using AND, OR, NOT, and XOR gates. How much simpler is this design than the design in part (a)