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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.
Fall 2010 ECE 331 - Digital System Design 2
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.
Fall 2010 ECE 331 - Digital System Design 3
Circuit Design
Spring 2011 ECE 331 - Digital System Design 4
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.
Spring 2011 ECE 331 - Digital System Design 5
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
Spring 2011 ECE 331 - Digital System Design 6
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
Spring 2011 ECE 331 - Digital System Design 7
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.
Spring 2011 ECE 331 - Digital System Design 8
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?
Spring 2011 ECE 331 - Digital System Design 9
Circuit Design: Example #1
Design in progress …
Spring 2011 ECE 331 - Digital System Design 10
Circuit Design: Example #2
Design a 7-Segment Decoder.
Spring 2011 ECE 331 - Digital System Design 11
Circuit Design: Example #2
7-SegmentDecoder
BCDNumber
7-Segment Display
4 inputs7 outputs
Spring 2011 ECE 331 - Digital System Design 12
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
Fall 2010 ECE 331 - Digital System Design 13
7-Segment Display
Fall 2010 ECE 331 - Digital System Design 14
7-Segment Display
Fall 2010 ECE 331 - Digital System Design 15
Circuit Design: Example #2
Design in progress …
Fall 2010 ECE 331 - Digital System Design 16
Circuit Analysis
Fall 2010 ECE 331 - Digital System Design 17
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.
Fall 2010 ECE 331 - Digital System Design 18
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.
Fall 2010 ECE 331 - Digital System Design 19
Circuit Analysis: Example
Analyze the following logic circuit:
1. Determine the Boolean expression2. Derive the truth table
A
B'
D'
E
C
F
Spring 2011 ECE 331 - Digital System Design 20
Questions?