Lecture 4- Combinational Logic

Lecture 4- Combinational Logic - ELEC151 Spring 2011 – L....

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Unformatted text preview: ELEC151 Spring 2011 – L. Yobas Lecture 4 – 1 Lecture 4 Combinational Logic ELEC151 Digital Circuits and Systems Spring 2011 Instructor: Levent Yobas ELEC151 Spring 2011 – L. Yobas Lecture 4 – 2 Lecture Overview Combinational circuits Design procedure and analysis skill Circuit examples XOR gates and Odd/Even parity circuits Equality/inequality functions Binary adder and subtractor Binary multiplier magnitude comparator Decoder and encoder Multiplexer and demultiplexer Reading Assignments: Chapter 4 ELEC151 Spring 2011 – L. Yobas Lecture 4 – 3 Combinational vs Sequential Logic Combinational Logic Outputs are solely determined by the inputs Represented by a truth table Sequential Logic (contains memory elements) There are feedbacks and clocks Outputs are determined by the inputs and feedbacks at clocks Represented by a state-transition diagram or flow chart Combinational Circuit Outputs Inputs Next-state Combinational Circuit Output Combinational Circuit Finite States Inputs Outputs Feedbacks Clocks ELEC151 Spring 2011 – L. Yobas Lecture 4 – 4 Design Procedures: Understand the project specifications Express the input and output relations in truth table In general (or multi-level logic), Derive the Boolean Expressions from the truth table Use Laws of Boolean Algebra for logic simplification In two-level logic, Re-express the truth table in the K-Map Read out the simplified Boolean expressions from the K-map Map the simplified Boolean expressions to digital circuits CAD tool simulation Implement the design by components Selections of components Digital design is more of an art than a science The creative spirit is critical in combining primitive elements in new ways to achieve a desired function. ELEC151 Spring 2011 – L. Yobas Lecture 4 – 5 Code Conversion Example Understand the specifications: BCD to Excess-3 Binary Coded Decimal (BCD) has 4 bits and 10 numbers Excess-3 code has a value that excesses 3 of BCD Express in a truth table (ABCD) 2 for the inputs and (WXYZ) 2 for the outputs BCD code Excess-3 code A B C D W X Y Z 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 ELEC151 Spring 2011 – L. Yobas Lecture 4 – 6 Code Conversion Example, K-map Re-express in the K-map Note the ABCD placement Incompletely specified functions Read out the most simplified Boolean expressions How many literals? 1+4+7+5=17 How many TTL gates? How many equivalent gates? ELEC151 Spring 2011 – L. Yobas Lecture 4 – 7 Code Conversion Example, Circuits Map the Boolean expressions to digital circuit in AND-OR (two-level), or some other forms (multi-level) The algebraical manipulation is possible, but not recommended ELEC151 Spring 2011 – L. Yobas Lecture 4 – 8 Common Combinational Logic...
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Lecture 4- Combinational Logic - ELEC151 Spring 2011 – L....

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