Design a combinational circuit with 4 inputs, A3, A2, A1, A0; 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 prime; and Z should be true if the number is a power of 2. As an example, if the input is A3A2A1A0= 1100, this represents the number 12, which is divisible by 3, not prime, and not a power of 2 so the outputs should be XYZ =100. 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)? (Please complete both a and b subquestions)

Design a combinational circuit with 4 inputs, A₃, A₂, A₁, A₀; 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 prime; and Z should be true if the number is a power of 2. As an example, if the input is A₃A₂A₁A₀= 1100, this represents the number 12, which is divisible by 3, not prime, and not a power of 2 so the outputs should be XYZ =100. 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)?

(Please complete both a and b subquestions)