Lecture 3 - Boolean Algebra

# Term where all input variables appear exactly once

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Unformatted text preview: = 33 m1 + m2 + m4 + m7 = { 1 ,2 ,4 ,7 } a¯ + abc + a¯c + abc ¯bc ¯ ¯ b¯ = Two-level logic (AND array followed by OR gate): a b c m1 m2 s m4 m7 January 24, 2013 Lecture 3 AWB FA - bit of carry minterm m0 = a¯c ¯b¯ a b cin cout = F (a, b, cout ) 0 0 0 0 m1 = a¯ ¯bc 0 0 1 0 m2 = abc ¯¯ 0 1 0 0 m3 = abc ¯ m4 = a¯c b¯ 0 1 1 1 1 0 0 0 m5 = a¯ bc 1 0 1 1 m6 = abc ¯ 1 1 0 1 m7 = abc 1 1 1 34 1 F (a, b, cin ) = m3 + m5 + m6 + m7 January 24, 2013 Lecture 3 AWB Systematic design - FA F (a, b, cin ) = 35 m3 + m5 + m6 + m7 = { 3 ,5 ,6 ,7 } abc + a¯ + abc + abc ¯ bc ¯ = a b cin m3 m5 cout m6 m7 January 24, 2013 Lecture 3 AWB Systematic design - simpliﬁcation 36 F (a, b, c) = abc + a¯ + abc + abc ¯ bc ¯ bc ¯ = abc + abc + a¯ + abc + abc ¯ = (¯ + a)bc + a¯ + abc + abc + abc a bc ¯ = bc + (¯ + b)ac + abc + abc b ¯ = bc + ac + ab(¯ + c) c = bc + ac + ab Is there any other way? January 24, 2013 Lecture 3 AWB Next .... 37 More Boolean algebra Karnaugh maps Read Sections 2.1-2.5 January 24, 2013 Lecture 3 AWB...
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## This note was uploaded on 09/26/2013 for the course ECE 2300 taught by Professor Long during the Fall '08 term at Cornell.

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