EE101Lecture5

# EE101Lecture5 - Lecture 5 Slides Binary Logic Boolean...

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© Mark Redekopp, All rights reserved Lecture 5 Slides Binary Logic Boolean Algebra Single Variable Theorems

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© Mark Redekopp, All rights reserved Digital Logic • Digital Logic is built on… Binary variables can be only one of two possible values (e.g. 0 or 1) Three operations on binary variables AND (all inputs true => output is true) OR (any inputs true => output is true) NOT (output is opposite of input)
© Mark Redekopp, All rights reserved Transistors The building blocks of logic gates (AND, OR, NOT) Electronic switches 2 positions (on/off, conducting/non-conducting) Output voltage of a transistor = high or low on off Controlling Input (Gate ) Output (Drain ) Source The voltage here determines if current can flow between drain and source A „ 1 ‟ here closes the switch Schematic Symbol of a Transistor Functional View of a Transistor as a Switch

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© Mark Redekopp, All rights reserved Transistors and Logic The connection of transistors determines the logical operation… In series (i.e. one after the next) = AND All transistors must be on to light up the light In parallel = OR Any transistor must be on to light up the light A B Voltage Source L L = A and B A B Voltage Source L L = A or B Transistors in SERIES = AND Transistors in PARALLEL = OR
© Mark Redekopp, All rights reserved Truth Tables Used to describe behavior of a digital circuit Show all possible combinations of inputs as a separate row in the table If n inputs => 2 n combinations / rows Show what the output should be for each input combination I 1 I 0 O 0 0 0 0 1 1 0 1 1 0 1 1 1 All possible input combinations Output value when inputs are 10

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© Mark Redekopp, All rights reserved AND, OR, NOT Gates NOT (Inverter) AND OR X Z X Y Z Z X Y X Y Z 0 0 0 0 1 0 1 0 0 1 1 1 X Y Z 0 0 0 0 1 1 1 0 1 1 1 1 X Z 0 1 1 0 Y X Z Y X Z ~X X X Z or or ' AND = „ALL‟ (true when ALL inputs are true) OR = „ANY‟ (true when ANY input is true)
© Mark Redekopp, All rights reserved NAND and NOR Gates NAND NOR Z X Y Z X Y Z 0 0 1 0 1 0 1 0 0 1 1 0 X Y X Y Z 0 0 1 0 1 1 1 0 1 1 1 0 Y X Z Y X Z X Y Z 0 0 0 0 1 0 1 0 0 1 1 1 X Y Z 0 0 0 0 1 1 1 0 1 1 1 1 AND NAND OR NOR True if NOT ANY input is true True if NOT ALL inputs are true

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© Mark Redekopp, All rights reserved XOR and XNOR Gates XOR Z X Y X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 XNOR Z X Y X Y Z 0 0 1 0 1 0 1 0 0 1 1 1 Y X Z Y X Z True if an odd # of inputs are true = True if inputs are different True if an even # of inputs are true = True if inputs are same
© Mark Redekopp, All rights reserved Gates Gates can have more than 2 inputs but the functions stay the same AND = output = 1 if ALL inputs are 1 Outputs 1 for only 1 input combination OR = output = 1 if ANY input is 1 Outputs 0 for only 1 input combination X Y Z F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 X Y Z F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 3-input AND 3-input OR F x y z F x y z

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## This note was uploaded on 12/02/2009 for the course EE 101 at USC.

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EE101Lecture5 - Lecture 5 Slides Binary Logic Boolean...

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