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ECE 301 – Digital Electronics 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.

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Spring 2011ECE 301 - Digital Electronics2 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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Spring 2011ECE 301 - Digital Electronics3 Circuit Design

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Spring 2011ECE 301 - Digital Electronics4 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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Spring 2011ECE 301 - Digital Electronics5 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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Spring 2011ECE 301 - Digital Electronics6 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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Spring 2011ECE 301 - Digital Electronics7 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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Spring 2011ECE 301 - Digital Electronics8 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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Spring 2011ECE 301 - Digital Electronics9 Circuit Design: Example #1 Design in progress …

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Spring 2011ECE 301 - Digital Electronics10 Circuit Design: Example #2 Design a 7-Segment Decoder.

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Spring 2011ECE 301 - Digital Electronics11 Circuit Design: Example #2 7-Segment Decoder BCD Number 7-Segment Display 4 inputs 7 outputs

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Spring 2011ECE 301 - Digital Electronics12 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

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Spring 2011ECE 301 - Digital Electronics13 7-Segment Display

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Spring 2011ECE 301 - Digital Electronics14 7-Segment Display

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Spring 2011ECE 301 - Digital Electronics15 Circuit Design: Example #2 Design in progress …

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Spring 2011ECE 301 - Digital Electronics16 Circuit Analysis

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Spring 2011ECE 301 - Digital Electronics17 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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Spring 2011ECE 301 - Digital Electronics18 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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Spring 2011ECE 301 - Digital Electronics19 Circuit Analysis: Example Analyze the following logic circuit: 1. Determine the Boolean expression 2. Derive the truth table A B' D' E C F

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Spring 2011ECE 301 - Digital Electronics20 Questions?

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