A Mealy Sequential circuit has one input x and one output z

A Mealy Sequential circuit has one input (x) and one output (z). z=1 if an only if the most recent input, combined with the preceding three inputs, was not a valid BCD encoding of a decimal digit; otherwise, z=0. Assume the BCD digits are received most significant bit first. Derive a state table for the circuit. (Seven states are sufficient) Repear for a Moore circuit (z=1 if and only if the previous four inputs were not a valid BCD digit). (Thirteen states are sufficient.)

Solution

In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs. (This is in contrast to a Moore machine, whose output values are determined solely by its current state.) A Mealy machine is a deterministic finite-state transducer: for each state and input, at most one transition is possible.