Design a circuit with a 4-bit input representing the binary number A3A2A1A0. The output should be 1 if the input value is divisible by 3. Assume that the circuit is to be used only for the digits 0 through 9 (thus, values for 10 to 15 can be don't care conditions).
a. Draw the Karnaugh map and truth table for the function.
b. Determine the minimum expression for the function.
c. Draw the circuit, using only AND, OR, and NOT gates.