1. A given system has four sensors (A, B, C and D) that can produce an output (Z) of 0 or 1. The system operates properly when exactly one of the sensors has its output equal to 1. An alarm must be raised when two or more sensors have the output of 1. Design the simplest circuit that can be used to raise the alarm. 2. Design a four-bit combinational circuit 2's complementer. The output of the circuit is the 2's complement of the input four-bit binary number. 3. Show that the circuit in Q2 can be constructed using only exclusive-OR gates. 4. A sequential circuit has two JK flip-flops A and B, two inputs x and y, and one output z. The flip-flop input equations and circuit output equation are JA = Bx + B'y' KA = B'xy' KB = A + xy' %3D JB = A'x z= Ax'y' + Bx'y' a. Draw the logic diagram of the circuit. b. Tabulate the state table. c. Draw the state diagram. d. Derive the state equations for A and B.