A sequential circuit has one input (X) and two outputs (S and V). X represents a 4-bit binary number N, which is input least significant bit first. S represents a 4-bit binary number equal to N + 2, which is output least significant bit first. At the time the fourth input occurs, V = 1 if N + 2 is too large to be represented by 4 bits; otherwise,
V = 0. The value of S should be the proper value, not a don’t care, in both cases. The circuit always resets after the fourth bit of X has been 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 D flip-flops and NAND gates. Repeat using NOR gates.