03LogicGates

t r u th ta b l e write up a table with all possible

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Unformatted text preview: e lle P in e a u ! ) T r u th ta b l e • Write-up a table with all possible input combinations, and check the output the output for each row. Inputs: Outputs: V1 V3 0 0 0 0 1 1 1 1 • V2 0 0 1 1 0 0 1 1 ACTIVITY 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 This is called a Truth Table. C O M P - 1 0 2 : C o m p u te r s a n d C o m p u tin g 5 ( th a n k s to J o e lle P in e a u ! ) C o m p a rin g lo g ic a l e x p re s s io n s • Recall our previous expression: ACTIVITY = (V1 AND V2) OR (V1 AND V3) OR (V2 AND V3) • You can also extract the logical expression directly from the Truth Table: ACTIVITY = ( (NOT V1) AND V2 AND V3) OR (V1 AND (NOT V2) AND V3) OR (V1 AND V2 AND (NOT V3)) OR (V1 AND V2 AND V3) C O M P - 1 0 2 : C o m p u te r s a n d C o m p u tin g 6 ( th a n k s to J o e lle P in e a u ! ) Extracting logical expression from the truth table • Recall: ACTIVITY = ( (NOT V1) AND V2 AND V3) OR (V1 AND (NOT V2) AND V3) OR (V1 AND V2 AND (NOT V3)) OR (V1 AND V2 AND V3) • How do we get this logical expression: – Consider each line in the table. • If th e lin e h a s O U T P U T = 1 , th is lin e m u s t b e in c lu d e d in th e lo g ic a l e x p r e s s io n a s a s u b - e x p r e s s io n . • T h e s u b - e x p r e s s io n in c lu d e s a ll v a r ia b le s , w h e r e t r u e v a r ia b le s a r e in c lu d e d w ith o u t m o d ific a tio n a n d n e g a tiv e v a r ia b le s a r e p r e c e d e d b y N O T o p e r a to r . • T h e v a r ia b le s in a s u b - e x p r e s s io n a r e s e p a r a te d b y “ A N D ” lo g ic a l o p e r a to r s . – Sub-expressions are separated by “OR” logical operators. – This is a “disjunction” of “conjunctions”. C O M P - 1 0 2 : C o m p u te r s a n d C o m p u tin g 7 ( th a n k s to J o e lle P in e a u ! ) P r o s / c o n s o f th e tw o l o g i c a l e x p r e s s i o n s • Compare: E1: ACTIVITY = (V1 AND V2) OR (V1 AND V3) OR (V2 AND V3) E2: ACTIVITY = ( (NOT V1) AND V2 AND V3) OR (V1 AND (NOT V2) AND V3) OR (V1 AND V2 AND (NOT V...
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This document was uploaded on 02/16/2014.

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