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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