Digital Lecture 8

# Digital Lecture 8 - 30-Jan-069:54 AM MSOP, MPOS,...

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30-Jan-06—9:54 AM 1 1 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo MSOP, MPOS, Simplification EEL 3701 1 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo EEL 3701 Menu • Minterms & Maxterms •SOP & POS • MSOP & MPOS • Simplification using the theorems/laws/axioms Look into my . .. EEL 3701 2 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo EEL 3701 Algebraic Simplification - Boolean Algebra Maxterms (written as M i ): A disjunctive (OR) term that is 0 in one and one only row of an exhaustive truth table. Minterms (written as m i ): A conjunctive (AND) term that is 1 in one and one only row of an exhaustive truth table. • Definitions (Review) Definition : Any function can be written as a product of sums that is as a conjunction of disjunctive terms (AND of ORs). Analogy: A minterm is like a column unit vector, u i , in 2 n space, (where n = number of Boolean Variables), e.g., m 2 =[0, 0, 1, 0] T (only one 1) Analogy: A maxterm is like a complement of a unit vector u i in 2 n space, e.g., M 2 =[1, 1, 0, 1] T (i.e., only one 0)

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30-Jan-06—9:54 AM 2 2 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo MSOP, MPOS, Simplification EEL 3701 3 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo EEL 3701 Algebraic Simplification - Boolean Algebra NOTE : M 0 = /m 0 i.e., M i = /m i f(A,B) A B G •Example : Suppose G = f(A,B) AB m 3 m 2 m 1 m 0 M 3 M 2 M 1 M 0 0 0 00011110 0 1 00101101 1 0 01001011 1 1 10000111 m i = minterm M i = maxterm EEL 3701 4 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo EEL 3701 POS & SOP Forms • Suppose G = True in 0th & 2nd rows • There are two possible ways of representing G: a) Look for 1’s: SOP (Sum Of Products; an OR of minterms) form
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## This note was uploaded on 09/11/2008 for the course EEL 3701c taught by Professor Gugel during the Spring '05 term at University of Florida.

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Digital Lecture 8 - 30-Jan-069:54 AM MSOP, MPOS,...

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