# Lect5 - 2 - SIMPLIFYING FUNCTIONS ON K-MAP Example...

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EE 316 - Digital Logic Design Lecture 5 Nur A. Touba University of Texas at Austin

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MINIMUM EXPRESSION Minimum Sum-of-Products Minimum number of terms Minimum number of literals Corresponds to minimum two-level gate circuit Minimum number of gates Minimum number of gate inputs Minimum Product-of-Sums Minimum number of factors Minimum number of literals
KARNAUGH MAPS Karnaugh Maps (K-maps) Like truth table, specified value of function for all combinations of variables Adjacent cells differ in only one variable

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3-VARIABLE K-MAP
3-VARIABLE K-MAP

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PLOTTING MINTERMS ON K-MAP Example: Plot F(a,b,c) = Σ m(1,5,7)
PLOTTING MAXTERMS ON K-MAP Example: Plot F(a,b,c) = Π M(0,2,3,4,6)

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PLOTTING TERMS ON K-MAP Examples
PLOTTING EXPRESSION ON K-MAP Example f(a,b,c) = abc + b’c’ + a’

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DERIVING EXPRESSION FROM K-MAP Example F(a,b,c) = Σ m(1,5,7)
DERIVING EXPRESSION FROM K-MAP Example F’(a,b,c) = [ Σ m(1,5,7)]’

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CONSENSUS THEOREM ON K-MAP Example ab + a’c + bc = ab + a’c
FUNCTION WITH TWO MINIMUM FORMS Example F(a,b,c) = Σ m(0,1,2,5,6,7)

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FOUR-VARIABLE K-MAP Example: F(a,b,c) = Σ m(1,4,7,13)
PLOTTING EXPRESSION ON K-MAP Example f(a,b,c,d) = acd + a’b + d’

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Unformatted text preview: SIMPLIFYING FUNCTIONS ON K-MAP Example f(a,b,c,d) = m(1,3,4,5,10,12,13) SIMPLIFYING FUNCTIONS ON K-MAP Example f(a,b,c,d) = m(1,3,4,5,7,9,12,13) SIMPLIFYING FUNCTIONS ON K-MAP Example f(a,b,c,d) = m(1,3,5,7,13,15) SIMPLIFYING FUNCTIONS ON K-MAP Example f(a,b,c,d) = m(1,3,4,6,9,10,11) SIMPLIFYING FUNCTIONS ON K-MAP Example f(a,b,c,d) = m(0,2,3,5,6,7,8,10,11,14,15) INCOMPLETELY SPECIFIED Example f(a,b,c,d) = m(1,3,5,7,9) + d(6,12,13) INCOMPLETELY SPECIFIED Example f(a,b,c,d) = m(1,3,5) + d(4,9,11) FINDING PRODUCT-OF-SUMS Example f = bd + acd + acd + bc EXAMPLE Use K-Map to Design Minimized Circuit Z = 1 iff two or more inputs of A, B, and C are 1 EXAMPLE Use K-Map to Design Minimized Circuit Z = 1 iff Even Number of Inputs of A, B, C, D are 1s All Input Combinations with More than Two 1s are Dont Cares EXAMPLE Design OR-AND Two-Level Minimal Circuit Z = 1 iff 2 or 3 Inputs of A,B,C,D are 1s ABCD is dont care...
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## This note was uploaded on 11/30/2010 for the course EE 316 taught by Professor Brown during the Fall '08 term at University of Texas at Austin.

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Lect5 - 2 - SIMPLIFYING FUNCTIONS ON K-MAP Example...

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