08 - 7-Sep-102:14 PM MSOP MPOS Simplification EEL 3701 EEL...

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7-Sep-10—2:14 PM MSOP, MPOS, Simplification 1 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo EEL 3701 EEL 3701 Menu • Minterms & Maxterms •SOP & POS • MSOP & MPOS • Simplification using the theorems/laws/axioms Look into my . .. 1 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo EEL 3701 EEL 3701 Algebraic Simplification - Boolean Algebra 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) Maxterms (written as M i ): A disjunctive (OR) term that is 0 in one and one only row of an exhaustive truth table. is 1 in one and one only row of an exhaustive truth table. 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) 2 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo Definition : Any function can be written as a product of sums that is as a conjunction of disjunctive terms (AND of ORs). 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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7-Sep-10—2:14 PM MSOP, MPOS, Simplification 2 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo EEL 3701 EEL 3701 Algebraic Simplification - Boolean Algebra •Example : Suppose G = f(A,B) f(A,B) A B G AB m 3 m 2 m 1 m 0 M 3 M 2 M 1 M 0 0 0 00011110 0 1 0 0 1 0 1 1 0 1 m i = minterm M i = maxterm 3 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo NOTE : M 0 = /m 0 i.e., M i = /m i 1 0 01001011 1 1 10000111 EEL 3701 EEL 3701 POS & SOP Forms • Suppose G = True in 0th & 2nd rows M 2 m 2 M 0 m 0 AB/ m 2 /M 2 /m 0 /M 0 GM 3 M 1 0 0 1001111 0 1 1010010 1 0 0110111 m i = /M i 4 University of Florida, EEL 3701 – File 08 © Drs. Schwartz & Arroyo • 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 09/11/2010 for the course EEL 3701c taught by Professor Gugel during the Spring '05 term at University of Florida.

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08 - 7-Sep-102:14 PM MSOP MPOS Simplification EEL 3701 EEL...

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