CSCE 211:Digital Logic Design

Chin-Tser Huanghuangct@cse.sc.edu

University of South Carolina

Chapter 7: The Design of Sequential Systems

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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.

Review: Design Process for Combinational Systems

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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).

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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.

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State Assignment of CE 6

We use assignment (a) in our discussion of CE6.

Design and Output Truth Table of CE6

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K-map for Next State

q1* = x q2 + x q1 q2* = x q2´ + x q1

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K-map for Output

z = q1 q2

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Therefore,D1 = x q2 + x q1

D2 = x q´2 + x q1

Design with D Flip Flops

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Implementation using D Flip Flops

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Design with JK Flip Flops

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J1 = xq2 K1 = x´ z = q1q2

J2 = x K2 = x´ + q´1

Design with JK Flip Flops

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T1 = x´q1 + xq´1q2 z = q1q2

T2 = x´q2 + xq´2 + xq´1q2

Design with T Flip Flops

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

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Example: 4-bit Binary Counter

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Design with JK Flip Flops

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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

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JA = KA = 1

JB = KB = x´A + xA´

JC = KC = x´BA + xB´A´

Design with JK Flip Flops

Design with JK Flip Flops

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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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