Tele 26 Sequential ircuits State epenent Present State Next State ompose of ombinational ircuits Storage Elements Often Require a lock Regular Pulse Train efinitions Perio With Rising Ege Trailing Ege The Spee of a Sequential ircuit is the Spee of the lock Sequential ircuits - Tele 26 uiling lock: Flip-Flops asic Unit of Sequential ircuits an ssume iscrete States State hanges a Function of the Inputs May or May Not e locke Sequential ircuits - 2
Tele 26 Set-Reset (SR) S S R Set Reset R x x Unefine Sequential ircuits - 3 Tele 26 Set-Reset with lock S S R Next State of x x No hange No hange Reset R Set Ineterminate Sequential ircuits - 4
Tele 26 (ata) Flip Flop Next State of x No hange = = Sequential ircuits - 5 Tele 26 - Flip Flop Next State of x x No hange No hange (=) Reset (=) Set (=) Invert State (=) Sequential ircuits - 6
Tele 26 T (Toggle) Flip Flop T T Next State of x No hange No hange (=) Invert State (=) Sequential ircuits - 7 Tele 26 Summary of Flip Flop haracteristic Tables S R (t+) T (t+) (t)??? (t) (t) (t+) (t) (t) (t+) Sequential ircuits - 8
Tele 26 nalysis proceure Ientify Inputs To the System To the Flip Flops Input Equations efine the Relationship etween the System Inputs an the FF Inputs Write State Table omponents Inputs States Outputs reate Relationships mong These omponents reate State iagrams Use for nalysis of Sequential ircuits Graphical Representation of the State Table Sequential ircuits - 9 Tele 26 Example Y 2 Z Y Y 2 Y Y 2 lock Sequential ircuits -
Tele 26 Example: Flip-Flop Input/Output Equations Flip Flop Input Equations =Y 2 =+Y 2 =Y Y 2 + Y 2 Output Equation: Z = Y Y 2 Sequential ircuits - Tele 26 Example: Flip-Flop Truth Tables Y Y 2 Y Y 2 Y Y 2 Y Y 2 Y (t+) Y Y 2 Y Y 2 Sequential ircuits - 2 Y 2 (t+)
Tele 26 Example: System Tables Transition Table State Table Output Table State Y Y 2 Y Y 2 (t+) Y Y 2 (t+) Z Sequential ircuits - 3 Tele 26 Example: State iagram / / / / / / / Format: Input/Output /Z / Sequential ircuits - 4
Tele 26 Sequential ircuit esign Proceure reate a State Table/State iagram From the Problem Statement erive Flip Flop Input Equations From the Next State onitions in the State Table erive Output Functions Simplify Use oolean lgebra Use -Maps raw Logic iagrams Sequential ircuits - 5 Tele 26 Example: Soa Machine Nee a System that Releases a ottle fter $.3 in oins Has een Receive Returns ppropriate hange Nickels imes Inputs Nickel ime uarter Sequential ircuits - 6
Tele 26 State iagram efinitions States = $. = $.5 = $. = $.5 E = $.2 F = $.25 G = $.5 Ege Labels N/RN,R,R N = Nickel, ime, uarter (Inputs) RN,R,R = Release Nickel, Release ime, Release ottle (Outputs) Sequential ircuits - 7 Tele 26 Example: State iagram States = =5 = =5 E=2 F=25 G=5 / (by clock) / G / / / / / F / / / / / / / / E / / / / Sequential ircuits - 8
Tele 26 Example: State Transition Table States = =5 = =5 E=2 F=25 G=5 Present E F Next State E F E F F G (Input (N)) Sequential ircuits - 9 Tele 26 Example: Observations an Strategy Given the Seven States Ientifie, it is Possible to Implement the System with log 2 7 = 3 Flip Flops Let us rbitrarily Select Flip Flops for This Project We Must Now Ientify the Transition Tables, Input Tables, an Output Tables for Each Flip Flop From These Tables, We an Write Input Output Equations an Reuce Them These Reuce Equations an Then be Use to Prouce a Logic iagram Sequential ircuits - 2
Tele 26 Example: Flip Flop Transition an Output Tables Present F/F Outputs Y Y 2 Y 3 (N) Next State (N) Output E F Y Y 2 Y 3 Y Y 2 Y 3 Y Y 2 Y 3 RN,R,R Y Sequential ircuits - 2 Tele 26 Example: Flip-Flop Transition Tables Y Flip Flop Y 2 Flip Flop 2 Y 3 Flip Flop 3 Sequential ircuits - 22
Tele 26 Example: Flip-Flop Input Tables What Inputs to Each Flip-Flop re Necessary to Prouce the Require Transition Tables? Y Y 2 Y 3 Flip Flop Flip Flop 2 2 2 3 3 Flip Flop 3 (t+) (t) (t) Sequential ircuits - 23 (t) (t+) Tele 26 Example: onclusion It is Now Possible to Write Separate Tables for Each Input:, 2, 3 an, 2, 3 From the Iniviual Tables, it is Possible to Write the Equation The Output Equations an be Written from the Output Table Presente Earlier Example: 2 2= YYY 2 3N + YYY 2 3N + YYY 2 3N + YYY 2 3N + YYYN 2 3 + YYY 2 3N Sequential ircuits - 24
Tele 26 uiling locks Using Sequential ircuits Registers Stanar Register Shift Register ounters inary Uses of ounters Event ounting Frequency ivier Sequential ircuits - 25 Tele 26 ata Registers Nee One Flip Flop for Each ata it -Type Flip Flops re Preferre Nee a Loa ontrol Signal Nee a lock Signal Sequential ircuits - 26
Tele 26 Four it ata Register I I I 2 I 3 Loa Sequential ircuits - 27 lock Tele 26 Shift Register Nee a Loa Signal Parallel Loa Serial Loa Nee a Shift Signal Shift Right Shift Left No Shift Nee a lock Signal Sequential ircuits - 28
Tele 26 Simple Four it Serial Loa Shift Register Input 2 3 4 Output lock ssume Positive Ege Triggere Flip-Flops Input Timing iagram 2 3 4 5 6 7 8 9 2 3 4 lock Sequential ircuits - 29 Tele 26 ounters esirable Features Loa lear ount Up or own Types of ounters Ripple ounters Pulses Ripple Through the ounter Variable State hanges cross ounter its inary ounters ll Flip Flops Use the Same lock onsistent State hange cross its Sequential ircuits - 3
Tele 26 Four it Ripple ounter 2 3 4 Event ssume Negative Ege Triggere Flip-Flops Event Timing iagram 2 3 4 5 6 7 8 9 2 3 4 Sequential ircuits - 3 Propagation elay Tele 26 Four it Synchronous inary ounter Event 2 3 4 ssume Positive Ege Triggere Flip-Flops lock Event Timing iagram 2 3 4 5 6 7 8 9 2 3 4 lock Sequential ircuits - 32