Lecture #8 - Minterm and Maxterm Expansions, Incompletely Specified Functions(2)

Lecture #8 - Minterm and Maxterm Expansions, Incompletely Specified Functions(2)

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ECE 301 – Digital Electronics Minterm and Maxterm Expansions, Incompletely Specified Functions
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Learning Objectives Minterms and Maxterms Minterm Expansions Canonical Sum of Products Maxterm Expansions Canonical Product of Sums Incompletely Specified Functions Design of combinational logic circuits from truth tables Spring 2012 2 ECE 301 - Digital
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Reading Roth & Kinney Sections 4.1 – 4.6 Spring 2012 ECE 301 - Digital 3
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Minterm A minterm , for a function of n variables, is a product term in which each of the n variables appears exactly once. Each variable may appear in its complemented or uncomplemented form. For a given row in the Truth table, the corresponding minterm is formed by Including the variable X, if X = 1. Including the complement of X, if X = 0. Spring 2012 ECE 301 - Digital 4
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Minterms Spring 2012 ECE 301 - Digital 5
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Minterms For example, m3 = A’BC Evaluates to 1 for A = 0, B = 1, and C = 1 Evaluates to 0 for all other combinations of A, B, and C. Spring 2012 ECE 301 - Digital 6 Each minterm evaluates to 1 for only one combination of the input variables.
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Minterm Expansion When a function F is written as the sum (ORing) of minterms it is referred to as the minterm expansion or standard sum of products . aka. canonical sum of products aka. disjunctive normal form If F = 1 for row i in the truth table, then mi must be present in the minterm expansion. The minterm expansion for function F is unique. However, it may not be a minimal solution (i.e. lowest cost) Spring 2012 ECE 301 - Digital 7
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Minterm Expansion The minterm expansion for a general function of 3 variables can be written as follows: Spring 2012 ECE 301 - Digital 8 ai = 0 or 1.
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This note was uploaded on 03/26/2012 for the course ECE 301 taught by Professor Staff during the Spring '08 term at George Mason.

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Lecture #8 - Minterm and Maxterm Expansions, Incompletely Specified Functions(2)

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