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Lecture 3 ECEN 248 - Boolean Logic Gates-Boolean Algebra.pdf

Lecture 3 ECEN 248 - Boolean Logic Gates-Boolean Algebra.pdf

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9/3/2017 1 ECEN 248 Lecture #3 – Boolean Logic Gates (cont); Boolean Algebra; Representing Boolean Functions Peng Li Department of Electrical and Computer Engineering Texas A&M University Digital Design 2e Copyright © 2010 Frank Vahid 2 Building Circuits Using Gates Recall Chapter 1 motion-in-dark example Turn on lamp (F=1) when motion sensed (a=1) and no light (b=0) F = a AND NOT(b) Build using logic gates, AND and NOT, as shown We just built our first digital circuit!
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9/3/2017 2 Digital Design 2e Copyright © 2010 Frank Vahid 3 Example: Converting a Boolean Equation to a Circuit of Logic Gates Q: Convert the following equation to logic gates: F = a AND NOT( b OR NOT(c) ) a b c F a Start from the output, work back towards the inputs Digital Design 2e Copyright © 2010 Frank Vahid 4 More examples Start from the output, work back towards the inputs a s d F ( a ) F = a AND (s OR d) 1 2 a a a b c F ( b ) F = (a AND NOT(b)) OR (b AND NOT(c)) 2 1 3
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9/3/2017 3 Digital Design 2e Copyright © 2010 Frank Vahid 5 Using gates with more than 2 inputs ( a ) ( b ) F = a AND b AND c a b F F a b c c Can think of as AND(a,b,c) Digital Design 2e Copyright © 2010 Frank Vahid 6 Example: Seat Belt Warning Light System Design circuit for warning light Sensors s=1: seat belt fastened k=1: key inserted Capture Boolean equation seat belt not fastened, and key inserted Convert equation to circuit Timing diagram illustrates circuit behavior We set inputs to any values Output set according to circuit w = NOT(s) AND k a a k s w BeltWarn Seatbelt time Inputs Outputs 1 1 1 0 0 0 k s w
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9/3/2017 4 Digital Design 2e Copyright © 2010 Frank Vahid 7 Gates vs. switches Notice Boolean algebra enables easy capture as an equation and then conversion to circuit How to design with switches? Of course, logic gates are built from switches, but we think at the level of logic gates, not switches w = NOT(s) AND k k s w BeltWarn Seatbelt BeltWarn w 1 0 0 1 s k a Digital Design 2e Copyright © 2010 Frank Vahid 8 More examples: Seat belt warning light extensions Only illuminate warning light if person is in the seat (p=1), and seat belt not fastened and key inserted w = p AND NOT(s) AND k k p s w Belt W a r n a Given t=1 for 5 seconds after key inserted. Turn on warning light when t=1 (to check that warning lights are working) w = (p AND NOT(s) AND k) OR t k w p s t BeltWarn a
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9/3/2017 5 Digital Design 2e Copyright © 2010 Frank Vahid 9 Some Gate-Based Circuit Drawing Conventions no yes not ok ok x y F no yes Typically don’t label signals Implicit directions – no need for arrows Two wires cannot be simply merged into just one Digital Design 2e Copyright © 2010 Frank Vahid 10 Boolean Algebra Boolean algebra precedence, highest precedence first. Symbol Name Description ( ) Parentheses Evaluate expressions nested in parentheses first NOT Evaluate from left to right * AND Evaluate from left to right + OR Evaluate from left to right 2.5
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9/3/2017 6 Digital Design 2e Copyright © 2010 Frank Vahid 11 Boolean Algebra Operator Precedence Evaluate the following Boolean equations, assuming a=1, b=1, c=0, d=1.
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