Digital Lecture 10 - 6-Feb-066:05 PM K-maps EEL 3701 EEL...

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6-Feb-06—6:05 PM 1 1 University of Florida, EEL 3701 – File 10 © Drs. Schwartz & Arroyo K-maps EEL 3701 1 University of Florida, EEL 3701 – File 10 © Drs. Schwartz & Arroyo EEL 3701 Menu • K-Maps and Boolean Algebra >Don’t cares >5 Variable K-maps Look into my . .. EEL 3701 2 University of Florida, EEL 3701 – File 10 © Drs. Schwartz & Arroyo EEL 3701 Karnaugh Maps - Boolean Algebra • We have discovered that simplification/minimization is an art. If you “see” it, GREAT! Else, work at it, work at it, …, … • A method to exhaustively minimize is due to Quine/McCluskey and is programmable. As the number of variables increase, it gets quite tedious and is not appropriate for our purposes Reminder Reminder X + /X=1 and XY+X /Y = X(Y + /Y) = X X + /X=1 and • Two terms which differ in only one literal can be minimized/ reduced by one literal. A K-Map is a graphical aid (a pattern recognition technique) for humans to implement the above two equations.
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6-Feb-06—6:05 PM 2 2 University of Florida, EEL 3701 – File 10 © Drs. Schwartz & Arroyo K-maps EEL 3701 3 University of Florida, EEL 3701 – File 10 © Drs. Schwartz & Arroyo EEL 3701 K-Maps Consider the following arrangement for f. Row cab f 0 0001 1 0011 2 0100 3 0111 4 1000 5 1011 6 1101 7 1110 abc = 0c = 1 00R 0 R 4 01R 1 R 5 11R 3 R 7 10R 2 R 6 Positions of Truth Table Rows in K-Map = = 1 001 0 011 1 111 0 100 1 But the minterms of function f are now rearranged so they differ in 1 literal. Look at row 1 (ab=01). The terms of function f differ only in one literal, e.g., f contains /a b /c + /a b c = /a b (/c + c) = /a b. In fact, any two adjacent rows or columns of 1’s differ in one literal, and thus, can be simplified. f SOP = /a /b /c + /a b /c + /a b c + a /b c + a b /c EEL 3701 4 University of Florida, EEL 3701 – File 10 © Drs. Schwartz & Arroyo EEL 3701 K-Maps ab c 01 00 1 0 01 1 1 11 1 0 10 0 1 • Now, consider the following arrangement for f . But the minterms of f are now arranged so they differ in 1 literal. abc f 000 1 001 0 010 1 011 1 100 0 101 1 110 1 111 0 m 0 m 5 Look at row 2. The terms of f differ only in one literal, e.g., f contains a’bc’+a’bc = a’b(c’+c)=a’b. In fact, if any of two rows or columns of 1’s differ in one literal, they can be simplified.
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Digital Lecture 10 - 6-Feb-066:05 PM K-maps EEL 3701 EEL...

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