A sequential circuit has one input (X) and two outputs (D and B). X represents a 4-bit binary number N, which is input least significant bit first. D represents a 4-bit binary number equal to N – 2, which is output least significant bit first. At the time the fourth input occurs, B = 1 if N - 2 is negative; otherwise, B = 0. The circuit always resets after the fourth bit of X is received.

(a) Derive a Mealy state graph and table with a minimum number of states (six states).
(b) Try to choose a good state assignment. Realize the circuit using J-K flip-flops and NAND gates. Repeat using NOR gates. (Work this part by hand.)