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CSCE 211: Digital Logic Design

Learn the step-by-step process to design sequential systems, including representation, simplification, implementation, and state assignment. Includes examples of binary counters and up/down counters.

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CSCE 211: Digital Logic Design

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  1. CSCE 211:Digital Logic Design Chin-Tser Huang huangct@cse.sc.edu University of South Carolina

  2. Chapter 7: The Design of Sequential Systems

  3. Review: Design Process for Combinational Systems Step 1: Represent each of the inputs and output in binary. Step 1.5: If necessary, break the problem into smaller subproblems. Step 2: Formalize the design specification either in the form of a truth table or of an algebraic expression. Step 3: Simplify the description. Step 4: Implement the system with the available components, subject to the design objectives and constraints.

  4. Design Process for Sequential Systems Step 1: From a word description, determine what needs to be stored in memory, that is, what are the possible states. Step 2: If necessary, code the inputs and outputs in binary. Step 3: Derive a state table or state diagram to describe the behavior of the system. Step 4: Choose a state assignment, that is, code the states in binary. Step 5: Choose a flip flop type and derive the flip flop input maps or tables. Step 6: Produce the logic equation and draw a block diagram (as in the case of combinational systems).

  5. Revisit Continuing Example 6 CE6. A system with one input x and one output z such that z = 1 iff x has been 1 for at least three consecutive clock times.

  6. State Assignment of CE 6 We use assignment (a) in our discussion of CE6.

  7. Design and Output Truth Table of CE6

  8. K-map for Next State q1* = x q2 + x q1 q2* = x q2´ + x q1

  9. K-map for Output z = q1q2

  10. Design with D Flip Flops Therefore, D1 = x q2 + x q1 D2 = x q´2 + x q1

  11. Implementation using D Flip Flops

  12. Design with JK Flip Flops

  13. Design with JK Flip Flops J1 = xq2 K1 = x´z =q1q2 J2 = x K2 = x´ + q´1

  14. Design with T Flip Flops T1 = x´q1 + xq´1q2 z =q1q2 T2 = x´q2 + xq´2 + xq´1q2

  15. Synchronous Counter • A synchronous counter is a device with no data input that goes through a fixed sequence of states on successive clocks • The output is often just the state of the system, i.e., the contents of all of the flip flops • So no output column is required in the state table

  16. Example: 4-bit Binary Counter

  17. Design with JK Flip Flops

  18. Another Example: Up/Down Counter • A counter that can count up or down according to a control input • Counts up when x=0 • Counts down when x=1

  19. Design with JK Flip Flops JA =KA = 1 JB =KB =x´A +xA´ JC =KC =x´BA +xB´A´

  20. Design with JK Flip Flops

  21. Another Example: Decimal Counter • A decimal counter goes through the sequence 0 1 2 3 4 5 6 7 8 9 0 1 … • Can you develop the truth table and then K-maps for the next state of each bit?

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