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Sequential Circuit Design. Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example.

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Presentation on theme: "Sequential Circuit Design. Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example."— Presentation transcript:

1 Sequential Circuit Design

2 Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example #3  Design of Synchronous Counters

3 Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example #3  Design of Synchronous Counters

4 Flip-flop Excitation Tables  Analysis: Starting from a circuit diagram, derive the state table or state diagram.  Design: Starting from a set of specifications (in the form of state equations, state table, or state diagram), derive the logic circuit.  Characteristic tables are used in analysis.  Excitation tables are used in design.

5 Flip-flop Excitation Tables  Excitation tables: given the required transition from present state to next state, determine the flip-flop input(s). JK Flip-flopSR Flip-flopD Flip-flopT Flip-flop

6 Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example #3  Design of Synchronous Counters

7 Sequential Circuit Design  Design procedure:  Start with circuit specifications – description of circuit behavior.  Derive the state table.  Perform state reduction if necessary.  Perform state assignment.  Determine number of flip-flops and label them.  Choose the type of flip-flop to be used.  Derive circuit excitation and output tables from the state table.  Derive circuit output functions and flip-flop input functions.  Draw the logic diagram.

8 Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example #3  Design of Synchronous Counters

9 Design: Example #1  Given the following state diagram, design the sequential circuit using JK flip-flops. 00 10 11 0 0 0 0 1 1 1 1 01

10 Design: Example #1  Circuit state/excitation table, using JK flip-flops. 00 10 11 0 0 0 01 11 1 01 0 X 1 X X 1 X 0 0 X 1 X X 0 X 1 JK Flip-flop’s excitation table. 0 X 1 X 0 X X 0 X 1

11 Design: Example #1  Block diagram. Combinational circuit A' A B B' x KAJAKBJB BB’AA’ External input(s) CP External output(s) (none) J QQ' KJ Q K What are to go in here?

12 Design: Example #1  From state table, get flip-flop input functions.

13 Design: Example #1  Flip-flop input functions. JA = B.x'JB = x KA = B.xKB = (A  x)'  Logic diagram: x B A CP J QQ' KJ Q K

14 Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example #3  Design of Synchronous Counters

15 Design: Example #2  Design, using D flip-flops, the circuit based on the state table below. (Exercise: Design it using JK flip-flops.)

16 Design: Example #2  Determine expressions for flip-flop inputs and the circuit output y. DA(A, B, x) =  m(2,4,5,6) DB(A, B, x) =  m(1,3,5,6) y(A, B, x) =  m(1,5)

17 Design: Example #2  From derived expressions, draw logic diagram: DA = A.B' + B.x' DB = A'.x + B'.x + A.B.x' y = B'.x D Q Q' D Q A A' B B' y CP x

18 Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example #3  Design of Synchronous Counters

19 Design: Example #3  Design with unused states. Given theseDerive these Unused state 000:

20 Design: Example #3  From state table, obtain expressions for flip-flop inputs.

21 Design: Example #3  From state table, obtain expressions for flip-flop inputs (cont’d).

22 Design: Example #3  From derived expressions, draw logic diagram: SA = B.xSB = A'.B'.xSC = x' RA = C.x'RB = B.C + B.x'RC = x y = A.x A A' B B' y CP x S Q Q'R S Q R S Q R C

23 Outline  Flip-flop Excitation Tables  Sequential Circuit Design  Design: Example #1  Design: Example #2  Design: Example #3  Design of Synchronous Counters

24 Design of Synchronous Counters  Counter: a sequential circuit that cycles through a sequence of states.  Binary counter: follows the binary sequence. An n-bit binary counter (with n flip-flops) counts from 0 to 2 n -1.  Example 1: A 3-bit binary counter (using T flip-flops). 001 000 111 010 011 100 110 101

25 Design of Synchronous Counters  3-bit binary counter (cont’d). TA 2 = A 1.A 0 A2A2 A1A1 A0A0 1 1 TA 1 = A 0 TA 0 = 1 A2A2 A1A1 A0A0 1 11 1 A2A2 A1A1 A0A0 111 1111 1

26 Design of Synchronous Counters  3-bit binary counter (cont’d). TA 2 = A 1.A 0 TA 1 = A 0 TA 0 = 1 1 A2A2 CP T Q T Q T Q A1A1 A0A0

27 Design of Synchronous Counters  Example 2: Counter with non-binary sequence: 000  001  010  100  101  110 and back to 000 001 000 010 100 110 101 JA = BJB = CJC = B' KA = BKB = 1KC = 1

28 Design of Synchronous Counters  Counter with non-binary sequence (cont’d). JA = BJB = CJC = B' KA = BKB = 1KC = 1 CP A 1 J QQ' KJ Q KJ Q K BC 001 000 010 100 110 101 111 011

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