Lecture04

# Lecture04 - ENGRD 2300 Introduction to Digital Logic Design...

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ENGRD 2300 Introduction to Digital Logic Design oolean Algebra Fall 2009 Boolean Algebra (Switching Algebra) Lecture 4: 1

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Announcements HW1 Will be posted soon This assignment is due Wed Sept 16 at 1:25pm, in the Homework Dropbox ab 2 has been posted on Blackboard Lab 2 has been posted on Blackboard Prelab for Lab 2 is due Fri Sept 11 at 1:25pm ring a paper copy of the lab instructions with you to Bring a paper copy of the lab instructions with you to lab For next class Read Wakerly 4.3 Lecture 4: 2
Minterms & Maxterms Lecture 4: 3 Minterms and Maxterms always contain all the variables

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Canonical Sums and Products A canonical sum is the sum of minterms corresponding to the on-set of a function E.g., F = Σ X,Y,Z (0,3,4,7) = X’•Y’•Z’ + X’•Y•Z + X•Y’•Z’ + X•Y•Z A canonical product is the product of maxterms orresponding to the ff et f a function corresponding to the off-set of a function E.g., F = Π X,Y,Z (1,2,5,6) (X+Y+Z’)•(X+Y’+Z)•(X’+Y+Z’)•(X’+Y’+Z) = (X+Y+Z’)•(X+Y’+Z)•(X’+Y+Z’)•(X’+Y’+Z) Conversion between maxterm and minterm list Lecture 4: 4 F = Σ X,Y,Z (0,3,4,7) = Π X,Y,Z (1,2,5,6)
Exercise What is Σ X,Y,Z (2,5) (as a Boolean expression)? What is Π C (2,5) (as a Boolean expression)? A,B,C Lecture 4: 5

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One-bit Adder Example One-Bit Binary Addition 00 1 1 1 Carry Out +0 0 +1 1 +0 1 +1 0 Multi-Bit Binary Addition AB a 3 b 3 A B a 2 b 2 A B a 1 b 1 A B a 0 b 0 C in C ou t S C in C ou t S C in C ou t S C in C ou t S Lecture 4: 6 s 3 s 2 s 1 s 0
Algebraic Simplification Example A B i Cout S 1-bit binary adder inputs: A, B, Carry-in Cin outputs: Sum, Carry-out Truth Table Æ Sum of minterms expression S = A'•B'•Cin + A'•B•Cin' + A•B'•Cin' + A•B•Cin 0 0 0 Cout S Cin B A 0 0 0 0 Cout S Cin B A 0 0 0 S Cout = A'•B•Cin + A•B'•Cin + A•B•Cin' + A•B•Cin 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 Lecture 4: 7 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1

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Use Theorems to Simplify Boolean Expressions oo ea p ess o s Apply theorems of Boolean algebra to simplify full adder's carry-out function
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Lecture04 - ENGRD 2300 Introduction to Digital Logic Design...

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