ECE 331 – Digital System Design

1. Circuit Design and Analysis (Lecture #9A) ECE 331 – Digital System Design 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.

2. ECE 331 - Digital System Design 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.

3. ECE 331 - Digital System Design Circuit Design

4. ECE 331 - Digital System Design 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.

5. ECE 331 - Digital System Design 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

6. ECE 331 - Digital System Design 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

7. ECE 331 - Digital System Design 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. Circuit Design: Example #1

8. ECE 331 - Digital System Design 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? Circuit Design: Example #1

9. ECE 331 - Digital System Design Design in progress … Circuit Design: Example #1

10. ECE 331 - Digital System Design Design a 7-Segment Decoder. Circuit Design: Example #2

11. ECE 331 - Digital System Design Circuit Design: Example #2 7 outputs 4 inputs BCD Number 7-Segment Decoder 7-Segment Display

12. ECE 331 - Digital System Design Binary Coded Decimal • A 4-bit code is used to represent each decimal digit.

13. ECE 331 - Digital System Design 7-Segment Display

14. ECE 331 - Digital System Design 7-Segment Display

15. ECE 331 - Digital System Design Design in progress … Circuit Design: Example #2

16. ECE 331 - Digital System Design Circuit Analysis

17. ECE 331 - Digital System Design 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.

18. ECE 331 - Digital System Design 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.

19. ECE 331 - Digital System Design Analyze the following logic circuit: 1. Determine the Boolean expression 2. Derive the truth table A B' C F D' E Circuit Analysis: Example

20. ECE 331 - Digital System Design Questions?