Digital Circuits and Systems

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1 EE201: Digital Circuits and Systems 4 Sequential Circuits page 1 of 11 EE201: Digital Circuits and Systems Section 4 Sequential Circuits 4.1 Overview of Sequential Circuits: Definition The circuit whose outputs and next state depend on both the input signals and the present state of the circuit Principle [spot the error!] Memory Elements Present Clock Input Signals Combinational Logic O S

2 EE201: Digital Circuits and Systems 4 Sequential Circuits page 2 of Flip-Flops SR Flip-Flop S R SET CLR JK Flip-Flop J K SET CLR D Flip-Flop D SET CLR S R X J K ! D S R X X 0 J K X X 1 0 X X 0 D X 0 0 X 1 1 T Flip-Flop DT SET CLR T 0 1! T

3 EE201: Digital Circuits and Systems 4 Sequential Circuits page 3 of Design of Sequential Circuits Algorithm: Obtain the description of circuit and create the Diagram Determine the Table Minimize the number of states Assign binary codes to each state Determine the number of flip-flops needed and give a letter symbol to each of them Choose the type of flip-flops Starting from Table, derive the Excitation Table and the Output Table Derive the minimized circuit output functions and flip-flop input functions Draw the Logic Diagram

4 EE201: Digital Circuits and Systems 4 Sequential Circuits page 4 of Example of Design Design a sequential logic circuit whose output Z is 1 except when the input X = 1 for at least four clock periods. Then the output Z is 0. Use J-K flip-flops. Diagram [X/Z] 1/1 1/1 1/1 A B C D 0/1 0/1 1/0 0/1 0/1 Coding Present Code A 0 0 B 0 1 C 1 0 D 1 1 Flip Flops We require two JK flip-flops. Let s name them JK A and JK B

5 EE201: Digital Circuits and Systems 4 Sequential Circuits page 5 of 11 Table Present Next Output Z X=0 X=1 X=0 X=1 A A B 1 1 B A C 1 1 C A D 1 1 D A D 1 0 Excitation Table A B X A B J A K A J B K B Z x 0 x x 1 x x x x x x 1 0 x x 0 1 x x 1 x x 0 x 0 0 J A Minimisations and Equations X\ A B x x x x J A = X B

6 EE201: Digital Circuits and Systems 4 Sequential Circuits page 6 of 11 K A X\ A B X x X x 0 0 K A = X J B X\ A B x x x x 1 J B = X K B X\ A B x 1 1 x 1 x 1 0 x K = X + = B A X A Z X\ A B Z = X A B

7 EE201: Digital Circuits and Systems 4 Sequential Circuits page 7 of Reduction Definition of Equivalent s Two or more states of a sequential circuit are equivalent if for the same values for the inputs, have exactly the same output and determine the sequential circuit transition to the same next state or to equivalent states. Algorithm for Reduction If more 2 or more states are equivalent, one of them can be substituted with the other one The other states that have transitions to one of the removed states have to have their next states changed into the remaining equivalent state Advantages of Reduction By reducing the number of states, it is possible that the number of flip-flops and/or amount of combinational circuitry needed to implement the sequential circuit will decrease, reducing the cost of the circuit

8 EE201: Digital Circuits and Systems 4 Sequential Circuits page 8 of 11 Example of Reduction Let s assume that there is the following state table: Present Next Output X=0 X=1 X=0 X=1 A A B 0 0 B C D 0 0 C A D 0 0 D E F 0 1 E A F 0 1 F G F 0 1 G A F 0 1 s G and E are equivalent (same next states for the same inputs and same outputs for the same inputs) reduction => state G will be replaced by E Present Next Output X=0 X=1 X=0 X=1 A A B 0 0 B C D 0 0 C A D 0 0 D E F 0 1 E A F 0 1 F E F 0 1

9 EE201: Digital Circuits and Systems 4 Sequential Circuits page 9 of 11 s D and F are equivalent reduction => state F will be replaced by D Present Next Output X=0 X=1 X=0 X=1 A A B 0 0 B C D 0 0 C A D 0 0 D E D 0 1 E A D 0 1 By reducing the number of states, the number of flip-flops and amount of combinational circuitry needed to implement this sequential circuit could have decreased, reducing the cost of the circuit. However in this example the number of flip-flops remains the same.

10 EE201: Digital Circuits and Systems 4 Sequential Circuits page 10 of Assignment Definition of Assignment The process of assigning a binary code to each state Possibilities for Assignment There are many possibilities to assign binary codes to states The number of possible options increases exponentially with the number of states The cost of the combinational circuit strongly depends on the state assignment chosen Although various Assignment methods have been proposed, there is no assignment procedure that guarantees a minimal cost for the resulting combinational circuit Examples of Assignment s Assign. 1 Assign. 2 Assign. 3 A B C D E

11 EE201: Digital Circuits and Systems 4 Sequential Circuits page 11 of Homework Having the following state table, design the sequential circuit following state assignment 1, 2 and 3, respectively. Present Next Output X=0 X=1 X=0 X=1 A A B 0 0 B C D 0 0 C A D 0 0 D E D 0 1 E A D 0 1

Chapter 14 Sequential logic, Latches and Flip-Flops

Chapter 14 Sequential logic, Latches and Flip-Flops Flops Lesson 4 JK Flip Flop Ch14L4-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 2 JK Flip-Flop ve edge triggered Output Q and