ECE 331 – Digital System Design

Circuit Design and Analysis

(Lecture #9A)

The slides included herein were taken from the materials accompanying Fundamentals of Logic Design, 6th Edition, by Roth and Kinney,

and were used with permission from Cengage Learning.

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Logic Circuits

Combinational Logic Circuits Output is a function of the inputs. Output is not a function of the order of the inputs. No memory is required.

Sequential Logic Circuits Output is a function of the state of the circuit and

the inputs. Output is a function of the history of the inputs. Requires memory.

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Circuit Design

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Circuit Design

For a given logic function, two two-level logic circuits can be realized.

An AND-OR (NAND-NAND) circuit An OR-AND (NOR-NOR) circuit

However, these two logic circuits do not necessarily have the same cost.

An objective of the digital circuit designer is to minimize the cost of the circuit to be built.

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Circuit Design Issues More than one circuit may meet the design

requirements. Solutions are, generally, not unique

Cannot always satisfy all of the requirements. Design tradeoffs must be identified and

considered. Cost Speed Power consumption

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Design Procedure

• Identify the requirements (i.e. circuit specifications)

• Determine the inputs and outputs

• Derive the truth table

• Determine the minterm and maxterm expansions

• Use K-maps (and Boolean algebra), to derive the minimum SOP and POS expressions

• Compare the costs of the two expressions

• Build (or synthesize) the “cheaper” circuit

• Verify the functional behavior of the circuit

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Circuit Design: Example #1

Design a combinational logic circuit that meets the following requirements:

1. Outputs a logic 1 for all values in the Fibonacci series between 0 and 7.

2. Outputs a logic 0 otherwise.

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Circuit Design: Example #1

Questions:

1. What is the Fibonacci Series?2. How many bits are needed to represent the input?3. How many bits are needed to represent the output?

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Circuit Design: Example #1

Design in progress …

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Circuit Design: Example #2

Design a 7-Segment Decoder.

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Circuit Design: Example #2

7-SegmentDecoder

BCDNumber

7-Segment Display

4 inputs7 outputs

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Binary Coded Decimal A 4-bit code is used to represent each decimal digit.

Decimal Digit Binary Code

0 0 0 0 0

1 0 0 0 1

2 0 0 1 0

3 0 0 1 1

4 0 1 0 0

5 0 1 0 1

6 0 1 1 0

7 0 1 1 1

8 1 0 0 0

9 1 0 0 1

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7-Segment Display

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7-Segment Display

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Circuit Design: Example #2

Design in progress …

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Circuit Analysis

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Circuit Analysis

Analyze a logic circuit to determine its behavior.

For a two-level circuit, the analysis process is simple. Boolean expression can often be written by inspection.

For multi-level circuits, the process is more complex. Cannot write a Boolean expression by inspection. Must follow a procedure to implement the analysis.

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Analysis Procedure

• Identify the circuit inputs and output(s).

• Track the logical behavior from input to output.

• Determine the Boolean expression for the output(s).

• Derive the truth table for the output(s).

• Evaluate the electrical and timing characteristics of the circuit.

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Circuit Analysis: Example

Analyze the following logic circuit:

1. Determine the Boolean expression2. Derive the truth table

A

B'

D'

E

C

F

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Questions?