\[ \newcommand{\bx}{\bar{x}} \newcommand{\by}{\bar{y}} \newcommand{\bz}{\bar{z}} \newcommand{\bA}{\bar{A}} \newcommand{\bB}{\bar{B}} \newcommand{\bC}{\bar{C}} \newcommand{\bD}{\bar{D}} \newcommand{\bE}{\bar{E}} \]

ECE 275: State reduction

Website: https://vikasdhiman.info/ECE275-Sequential-Logic/


  • Midterm 2 postponed to Nov 15th instead of Nov 8th.
  • HW 8 is posted is due next Wednesday (Nov 10th) at 9 AM before class.

Ex2: Parity Checker

Ex2: Parity Checker using T flip-flops

Ex2: Parity Checker using J-K flip-flops

Ex2: Parity Checker

State reduction: Ex1

A sequential circuit has one input (X) and one output (Z). The circuit examines groups of four consecutive inputs and produces an output \( Z = 1 \) if the input sequence 0101 or 1001 occurs. The circuit resets after every four inputs. Find the Mealy state graph.

State reduction: Ex1

State reduction

Equivalent states

Let \( N_1 \) and \( N_2 \) be sequential circuits (not necessarily different). Let \( \underline{X} \) represent a sequence of inputs of arbitrary length. Then state p in \( N_1 \) is equivalent to state q in \( N_2 \) iff \( \lambda_1(p, \underline{X} ) = \lambda_2 (q, \underline{X}) \) for every possible input sequence.

Equivalent states

Two states p and q of a sequential circuit are equivalent iff for every single input X, the outputs are the same and the next states are equivalent, that is, \( \lambda(p, X) = \lambda(q, X) \) and \( \phi(p, X) = \phi(q, X) \).

Implication tables: Ex2

Implication tables

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