Sequential Circuit Analysis 91509 L 21 Sequential Circuit

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Sequential Circuit Analysis 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne

Sequential Circuit Analysis 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 1

Class 21 -Sequential Circuit Analysis o Design of a simple sequential circuit Analysis of

Class 21 -Sequential Circuit Analysis o Design of a simple sequential circuit Analysis of an existing circuit o Material from section 5 -4 of text + o 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 2

State machine synthesis o o o Creation of state machine State machines are digital

State machine synthesis o o o Creation of state machine State machines are digital sequential circuits that transition through a series of states according to their design. For the creation of any such circuit always start with the problem definition or the circuit specification. 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 3

Problem Statement o o Design a 2 bit up counter that has no preset

Problem Statement o o Design a 2 bit up counter that has no preset state and continually cycles thought the 4 states. This can be defined by a table – called a state table. n n n Present State 00 01 10 11 9/15/09 - L 21 Sequential Circuit Analaysis Next State 01 10 11 00 Copyright 2009 - Joanne De. Groat, ECE, OSU 4

A diagram representation o This form is termed a state diagram 9/15/09 - L

A diagram representation o This form is termed a state diagram 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 5

Sequential circuits o Basic form and elements 9/15/09 - L 21 Sequential Circuit Analaysis

Sequential circuits o Basic form and elements 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 6

This problem o o Storage Elements – 2 Flip-flops No inputs Current state is

This problem o o Storage Elements – 2 Flip-flops No inputs Current state is the output Combination logic generate the next state value. 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 7

Generating Next State o Use K maps generated from State Table 9/15/09 - L

Generating Next State o Use K maps generated from State Table 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 8

The Circuit o Using D FF 9/15/09 - L 21 Sequential Circuit Analaysis Copyright

The Circuit o Using D FF 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 9

Sequential Circuit analysis o The circuit to analyze o How to start? o How

Sequential Circuit analysis o The circuit to analyze o How to start? o How about with the next state equations? 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 10

Next State Equations o For DA have an AND-OR set of gates to generate

Next State Equations o For DA have an AND-OR set of gates to generate the input. n n n o The upper AND gate has inputs X and A The lower AND gate has inputs X and B So DA = AX + BX For DB have a single AND gate whose inputs are X and A’ n So 9/15/09 - L 21 Sequential Circuit Analaysis DB = A’X Copyright 2009 - Joanne De. Groat, ECE, OSU 11

Also have an output Y o o The OR gate has inputs A and

Also have an output Y o o The OR gate has inputs A and B This feeds into a 2 -input AND gate whose other input is X’ Thus Y = (A+B)X’ Now having these equations can construct the state table for the state machine 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 12

The state table o For generation of the next state you have the Present

The state table o For generation of the next state you have the Present State as indicated by A and B plus the input X. This next state becomes the current state on the clock. 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 13

Another form of the state table o Two-dimensional form of the same table 9/15/09

Another form of the state table o Two-dimensional form of the same table 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 14

The state Diagram o o The state diagram for this systems is Not the

The state Diagram o o The state diagram for this systems is Not the notation on the diagram n On transition arcs – input/output 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 15

Class 21 assignment o o Covered sections 5 -4 Problems for hand in n

Class 21 assignment o o Covered sections 5 -4 Problems for hand in n o Problems for practice n o 5 -6 and 5 -10 5 -7, 5 -8, 5 -9 Reading for next class: sections 5 -5 9/15/09 - L 21 Sequential Circuit Analaysis Copyright 2009 - Joanne De. Groat, ECE, OSU 16