A sequential circuit has a single input (X) and a single

Chapter 15, Problem 15.13

(choose chapter or problem)

A sequential circuit has a single input (X) and a single output (Z). The circuit examines each disjoint block of four inputs and determines whether the block is a valid BCD representation of a decimal digit; if not, Z = 1. State \(S_0\) is the initial state, and the circuit enters state \(S_0\) after the fourth input. The BCD digits are received most significant bit first. The following state table was constructed as a Mealy table using a sufficient number of states to remember the last three inputs with the output produced when the fourth input bit of a block is received.

(a) Does the resulting table specify a Mealy or a Moore circuit?

(b) Reduce the state table to a minimum number of states. (Hint: Use the simple example of state equivalence used in Section 15.1 to eliminate as many states as possible.)

(c) For each state in the reduced table, give the input pattern remembered by that state.