Lecture #6 - Introduction to Combinational logic circuits, Boolean expressions, Truth tables

# Lecture #6 - Introduction to Combinational logic circuits, Boolean expressions, Truth tables

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ECE 301 – Digital Electronics Introduction to Combinational logic circuits, Boolean expressions, and Truth tables

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Learning Objectives Introduction to combinational logic circuits Boolean expressions Truth tables Analysis of combinational logic circuits Logical analysis Timing analysis Design of combinational logic circuits Circuit and wiring diagrams Spring 2012 ECE 301 - Digital 2
Reading Roth & Kinney, Section 2.3 Spring 2012 ECE 301 - Digital 3

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Combinational Logic Circuits Composed of interconnected logic gates. Graphical representation of a logic function. Can be designed from (or described by) Truth tables Boolean expressions Realized through Interconnection of discrete components. Spring 2012 4 ECE 301 - Digital
Combinational Logic Circuits Spring 2012 ECE 301 - Digital 5 circuit inputs circuit output literals logical operators

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Logic Functions A logic function can be represented by Circuit diagram (aka. Logic circuit) Boolean expression Truth table Spring 2012 ECE 301 - Digital 6
Truth Tables A truth table defines the output of a logic function for each combination of the input variables. Each row in the truth table corresponds to a unique combination of the input variables. For n input variables, there are 2n rows Each row is assigned a numerical value, with rows listed in ascending order. The order of the input variables defined in the logic function is important! Spring 2012 ECE 301 - Digital 7

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Truth Tables Row # A B C F(A,B,C) 0 0 0 0 1 0 0 1 2 0 1 0 3 0 1 1 4 1 0 0 5 1 0 1 6 1 1 0 7 1 1 1 Spring 2012 ECE 301 - Digital 8 3-variable Truth Table
Truth Tables Row # A B C D F(A,B,C,D ) 0 0 0 0 0 1 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 12 1 1 0 0 13 1 1 0 1 14 1 1 1 0 15 1 1 1 1 Spring 2012 ECE 301 - Digital 9 4-variable Truth Table

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Truth Tables Row # A B C F1(A,B, C) 0 0 0 0 0 1 0 0 1 1 2 0 1 0 1 3 0 1 1 0 4 1 0 0 0 5 1 0 1 0 6 1 1 0 1 7 1 1 1 0 Spring 2012 ECE 301 - Digital 10 Row # A B C F2(A,B, C) 0 0 0 0 1 1 0 0 1 0 2 0 1 0 1 3 0 1 1 0 4 1 0 0 0 5 1 0 1 1 6 1 1 0 1 7 1 1 1 0 Are the two logic functions equivalent?
Boolean Expressions A Boolean expression consists of Literals – variables and their complements Logical operations Examples: F1 = A.B.C + A’.B.C’ + A.B’.C’ F2 = (A’+B’+C).(A+B+C).(A’+B+C’) F3 = A.(B+C’) + A’.B’.C’ + (A’+C).B Spring 2012 ECE 301 - Digital 11

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## This note was uploaded on 03/26/2012 for the course ECE 301 taught by Professor Staff during the Spring '08 term at George Mason.

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Lecture #6 - Introduction to Combinational logic circuits, Boolean expressions, Truth tables

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