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Lecture04

# Lecture04 - Announcements ECE 2300 Introduction to Digital...

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Lecture 4: Spring 2010 1 ECE 2300 Introduction to Digital Logic Design Combinational Logic Minimization Lecture 4: 2 Announcements • HW 2 is on Blackboard Lecture 4: 3 Canonical Sums and Products Canonical sum : The sum of minterms corresponding to the on-set – F = ! X,Y,Z (0,3,4,7) = X’•Y’•Z’ + X’•Y•Z + X•Y’•Z’ + X•Y•Z Canonical product : The product of maxterms corresponding to the off-set – F = ! X,Y,Z (1,2,5,6) = (X+Y+Z’)•(X+Y’+Z)•(X’+Y+Z’)•(X’+Y’+Z) • F = ! X,Y,Z (0,3,4,7) = ! X,Y,Z (1,2,5,6) XY Z F 000 001 010 011 100 101 110 111 1 0 0 1 1 0 0 1 Lecture 4: 4 Combinational Logic Outputs depend only on current inputs – Example: Detect if the input is a prime number In contrast, sequential logic has “state” – Example: Detect if the last two inputs in a row are prime numbers – We’ll cover sequential logic later Lecture 4: 5 Combinational Logic Synthesis Given a functional requirement, realize a circuit that implements that functionality General approach – Step 1: Identify functions – Step 2: For each function • Obtain canonical form • Minimize the expression Lecture 4: 6 A B Cin Cout S Cout = A'•B•Cin + A•B'•Cin + A•B•Cin' + A•B•Cin S = A'•B'•Cin + A'•B•Cin' + A•B'•Cin' + A•B•Cin 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 Cout S Cin B A Algebraic Simplification Example • 1-bit binary adder – inputs: A, B, Carry-in – outputs: Sum, Carry-out • Truth Table ! Canonical sum Lecture 4: 7 Cout = A'•B•Cin + A•B'•Cin + A•B•Cin' + A•B•Cin = A'•B•Cin + A•B'•Cin + A•B•Cin' + A•B•Cin + A•B•Cin ( idempotency ) = A'•B•Cin +A•B•Cin + A•B'•Cin + A•B•Cin' + A•B•Cin ( commutativity ) = (A' + A)•B•Cin + A•B'•Cin + A•B•Cin' + A•B•Cin ( distributivity ) =

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Lecture04 - Announcements ECE 2300 Introduction to Digital...

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