04 sequential circuits
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This document provides an overview of sequential circuits, including their definition, principles, memory elements, flip-flops, and the design process. It discusses the algorithm for designing sequential circuits, which involves obtaining the description, creating a state diagram and table, minimizing states, assigning codes, choosing flip-flops, deriving tables, and drawing the logic diagram. An example design is presented to illustrate the process. State reduction and state assignment are also covered.
![EE201: Digital Circuits and Systems 4 Sequential Circuits page 1 of 11
EE201: Digital Circuits and Systems
Section 4 ¨C 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
Combinational Logic
Present
State
Input
Signals
O
S
Clock](https://image.slidesharecdn.com/04sequentialcircuits-180803061709/85/04-sequential-circuits-1-320.jpg)
![EE201: Digital Circuits and Systems 4 Sequential Circuits page 4 of 11
4.4 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.
? State Diagram [X/Z]
A B C D
1/1 1/1 1/1
0/1
0/1
0/1
0/1 1/0
? State Coding
Present
State
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 JKA and JKB](https://image.slidesharecdn.com/04sequentialcircuits-180803061709/85/04-sequential-circuits-4-320.jpg)
04 sequential circuits
- 1. EE201: Digital Circuits and Systems 4 Sequential Circuits page 1 of 11 EE201: Digital Circuits and Systems Section 4 ¨C 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 Combinational Logic Present State Input Signals O S Clock
- 2. EE201: Digital Circuits and Systems 4 Sequential Circuits page 2 of 11 4.2 Flip-Flops SR Flip-Flop Q Q SET CLR S R JK Flip-Flop J Q Q K SET CLR D Flip-Flop Q Q SET CLR D T Flip-Flop Q Q SET CLR DT S R Q¡¯ 0 0 Q 0 1 0 1 0 1 1 1 X Q Q¡¯ S R 0 0 0 X 0 1 1 0 1 0 0 1 1 1 X 0 J K Q¡¯ 0 0 Q 0 1 0 1 0 1 1 1 !Q Q Q¡¯ J K 0 0 0 X 0 1 1 X 1 0 X 1 1 1 X 0 D Q¡¯ 0 0 1 1 Q Q¡¯ D X 0 0 X 1 1 Q Q¡¯ T 0 0 0 0 1 1 1 0 1 1 1 0 T Q¡¯ 0 Q 1 !Q
- 3. EE201: Digital Circuits and Systems 4 Sequential Circuits page 3 of 11 4.3 Design of Sequential Circuits Algorithm: ? Obtain the description of circuit and create the State Diagram ? Determine the State 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 State 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 11 4.4 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. ? State Diagram [X/Z] A B C D 1/1 1/1 1/1 0/1 0/1 0/1 0/1 1/0 ? State Coding Present State 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 JKA and JKB
- 5. EE201: Digital Circuits and Systems 4 Sequential Circuits page 5 of 11 ? State Table Next State Output ZPresent State 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 QA QB X Q¡¯A Q¡¯B JA KA JB KB Z 0 0 0 0 0 0 x 0 x 1 0 0 1 0 1 0 x 1 x 1 0 1 0 0 0 0 x x 1 1 0 1 1 1 0 1 x x 1 1 1 0 0 0 0 x 1 0 x 1 1 0 1 1 1 x 0 1 x 1 1 1 0 0 0 x 1 x 1 1 1 1 1 1 1 x 0 x 0 0 ? Minimisations and Equations JA X QA QB 00 01 11 10 0 0 0 x x 1 0 1 x x BA XQJ =
- 6. EE201: Digital Circuits and Systems 4 Sequential Circuits page 6 of 11 KA X QA QB 00 01 11 10 0 X x 1 1 1 X x 0 0 XKA = JB X QA QB 00 01 11 10 0 0 x x 0 1 1 x x 1 XJB = KB X QA QB 00 01 11 10 0 x 1 1 x 1 x 1 0 x AAB XQQXK =+= Z X QA QB 00 01 11 10 0 0 0 0 0 1 0 0 1 0 BAQXQZ =
- 7. EE201: Digital Circuits and Systems 4 Sequential Circuits page 7 of 11 4.5 State Reduction Definition of Equivalent States ? 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 State 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 State 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 State Reduction ? Let¡¯s assume that there is the following state table: Next State OutputPresent State 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 ? States G and E are equivalent (same next states for the same inputs and same outputs for the same inputs) ? State reduction => state G will be replaced by E Next State OutputPresent State 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 ? States D and F are equivalent ? State reduction => state F will be replaced by D Next State OutputPresent State 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 11 4.6 State Assignment Definition of State Assignment ? The process of assigning a binary code to each state Possibilities for State 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 State Assignment methods have been proposed, there is no assignment procedure that guarantees a minimal cost for the resulting combinational circuit Examples of State Assignment States Assign. 1 Assign. 2 Assign. 3 A 0 0 1 0 0 0 0 0 0 B 0 1 0 0 1 0 1 0 0 C 0 1 1 0 1 1 0 1 0 D 1 0 0 1 0 1 1 0 1 E 1 0 1 1 1 1 0 1 1
- 11. EE201: Digital Circuits and Systems 4 Sequential Circuits page 11 of 11 4.7 Homework ? Having the following state table, design the sequential circuit following state assignment 1, 2 and 3, respectively. Next State OutputPresent State 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