Consider circuit with 4 input bits whose output is 1 if the input is divisible by 3. Find minimal sum of products expression for circuit.

create a circuit for Full Adder S=A'B'C'in+A'BCin+AB'Cin+ABC'in

PROBLEM 2 4-bit decrement In class we considered an increment circuit that adds 1 to its input value. Now we want a circuit that subtracts 1 (i.e., z = x − 1). Draw a 4-bit decrement circuit that does not use not gates. -

Implement the following circuits only using NAND gates. Use the method of your choice (pushing bubbles, De Morgan's, etc.) a. f(A,B)=(A′+B′)