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Combinational Logic Circuits Reference: M. Mano, C. Kime, “Logic and Computer Design Fundamentals”, Chapter 2 Dr. Costas Kyriacou and Dr. Konstantinos Tatas

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 2 Basic Logic Gates Truth Table Logic Expression Gate Symbol Logic Function

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 3 Basic Logic Gates with Inverted Outputs

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 4 Logic Gates with more than two inputs

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 5 Circuit Implementation of a Logic Expression with Gates

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 6 Circuit Implementation of Logic Expressions:- Examples

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 7 Circuit Implementation of Logic Expressions:- Homework

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 8 Truth Tables Truth table of a logic circuit is a table showing all the possible input combinations with the corresponding value of the output. Examples:

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 9 Truth Tables: Examples

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 10 Minterms and maxterms RowXYZFMintermMaxterm 0000F(0,0,0)X΄Y΄Z΄X΄Y΄Z΄Χ+Υ+Ζ 1001F(0,0,1)X΄Y΄ZX΄Y΄ZΧ+Υ+Ζ΄ 2010F(0,1,0)X΄YZ΄Χ+Υ΄+Ζ 3011F(0,1,1)X΄YZΧ+Υ΄+Ζ΄ 4100F(1,0,0)XY΄Z΄Χ΄+Υ+Ζ 5101F(1,0,1)XY΄ZΧ΄+Υ+Ζ΄ 6110F(1,1,0)XYZ΄Χ΄+Υ΄+Ζ 7111F(1,1,1)XYZΧ΄+Υ΄+Ζ΄

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 11 Standard forms: Sum of Products

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 12 Logic expression and truth table of a logic circuit

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 13 Example: Find the logic expression and fill up the truth table for the circuit below.

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 14 Homework: Find the logic expression and fill up the truth table for the circuit below.

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 15 Analyzing a logic circuit using timing diagrams Logic 0 Logic 1

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 16 Homework: Fill up the truth table and timing diagram for the circuit below.

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 17 Boolean Algebra Basic Boolean identities:

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 18 Boolean Algebra (Examples) Prove the following identities using Boolean algebra and truth tables:

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 19 Digital circuit simplification using Boolean algebra Logic functions are simplified in order to reduce the number of gates required to implement them. Thus the circuit will –cost less, –need less space and power, –be build faster with less effort. For example the expression F needs six gates to be build. If the expression is simplified then the function can be implemented with only two gates.

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 20 Boolean Algebra (Examples) Simplify the expressions given below. Use truth tables to verify your results.

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 21 Boolean Algebra (Examples - Cont.) Simplify the expressions given below. Use truth tables to verify your results.

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 22 Boolean Algebra (Examples - Cont.) Simplify the expression given below. Use truth tables to verify your results.

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ACOE161ACOE161 - Digital Logic for Computers - Frederick University 23 Boolean Algebra (Examples - Cont.) Simplify the expression given below. Use truth tables to verify your results.

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