1. 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, 6 th Edition, by Roth and Kinney, and were used with permission from Cengage Learning.

2. Fall 2010ECE 331 - Digital System Design2 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. Fall 2010ECE 331 - Digital System Design3 Circuit Design

4. Spring 2011ECE 331 - Digital System Design4 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. Spring 2011ECE 331 - Digital System Design5 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. Spring 2011ECE 331 - Digital System Design6 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. Spring 2011ECE 331 - Digital System Design7 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.

8. Spring 2011ECE 331 - Digital System Design8 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?

9. Spring 2011ECE 331 - Digital System Design9 Circuit Design: Example #1 Design in progress …

10. Spring 2011ECE 331 - Digital System Design10 Circuit Design: Example #2 Design a 7-Segment Decoder.

11. Spring 2011ECE 331 - Digital System Design11 Circuit Design: Example #2 7-Segment Decoder BCD Number 7-Segment Display 4 inputs 7 outputs

12. Spring 2011ECE 331 - Digital System Design12 Binary Coded Decimal A 4-bit code is used to represent each decimal digit. Decimal DigitBinary Code 00 0 10 0 0 1 20 0 1 0 30 0 1 1 40 1 0 0 50 1 60 1 1 0 70 1 1 1 81 0 0 0 91 0 0 1

13. Fall 2010ECE 331 - Digital System Design13 7-Segment Display

14. Fall 2010ECE 331 - Digital System Design14 7-Segment Display

15. Fall 2010ECE 331 - Digital System Design15 Circuit Design: Example #2 Design in progress …

16. Fall 2010ECE 331 - Digital System Design16 Circuit Analysis

17. Fall 2010ECE 331 - Digital System Design17 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. Fall 2010ECE 331 - Digital System Design18 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. Fall 2010ECE 331 - Digital System Design19 Circuit Analysis: Example Analyze the following logic circuit: 1. Determine the Boolean expression 2. Derive the truth table A B' D' E C F

20. Spring 2011ECE 331 - Digital System Design20 Questions?