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)
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© 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 All transistors must be on to light up the light – In parallel = OR Any Any transistor must be on to light up the light Transistors in SERIES = AND Transistors in PARALLEL = OR
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© 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 XZ X Y ZZ 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)
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© Mark Redekopp, All rights reserved NAND and NOR Gates NAND NOR Z X Y Z
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EE101Lecture5 - Lecture 5 Slides Binary Logic Boolean...

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