M16_2_EEM16_F11_L03

M16_2_EEM16_F11_L03 - in which each of the n variables...

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EEM16/CSM51A: Logic Design of Digital Systems Lecture #3 Specification of Combinational System Prof. Danijela Cabric Fall 2011
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Agenda ± Switching Functions and Expressions ± Sum of products and sum of minterms ± Product of sums and product of maxterms 2
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Specification at Binary Level 3
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Switching Functions 4
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Example Switching Function for n=3 5
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Tabular Representation of Switching Functions: Truth Tables 6
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Switching Functions of One Variable 7
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Switching Functions of Two Variables 8
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Composition of Switching Functions 9
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Switching Expressions 10
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Switching Algebra and Expression Evaluation 11
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Representing Switching Functions by Switching Expressions 12
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Representation of Well know Switch Functions as Switching Expressions 13
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Graphical Representations as Gate Symbols 14
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Graphical Representations as Gate Symbols (contd.) 15
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Equivalent Switching Expressions 16
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Equivalence Classes 17
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Algebraic Method of Obtaining Equivalent Expressions 18
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Example: Show that E1 and E2 are equivalent 19
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Sum of Products (SoP) Form 20
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Minterm 21 ± For a Boolean function of n variables x1, …, xn, a product term
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Unformatted text preview: in which each of the n variables appears once (either complemented, or uncomplemented) is called a minterm There are 2 n minterms of n variables Example: 22 Indexing Minterms Minterm m j indexed by integer j= i=0,,n 1 x i 2 i 23 Minterm Functions 24 Example: E(x2, x1, x0) = m1+m2+m6 = m(1,2,6) Example: Table Sum of Products (Minterms) 25 26 Dual: Product of Sums (PoS) Form 27 Maxterms For a boolean function of n variables x1, , xn, a sum term in which each of the n variables appears once (either complemented, or uncomplemented) is called a maxterm Examples 28 Indexing Maxterms Maxterm M j indexed by integer j= i=0,,n 1 x i 2 i 29 Example: E(x2, x1, x0) = M0 M5 M6 = M(0,5,6) Example: Table Product of Sums (Maxterms) 30 31 Conversion Among Canonical Forms Example 2.18: Lock Control 32 Coding 33 Binary Specification 34 Switching Expressions 35 Example 2.19: Radix 4 Comparator 36...
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This note was uploaded on 04/02/2012 for the course EE EEM16 taught by Professor Cabriv during the Fall '11 term at UCLA.

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M16_2_EEM16_F11_L03 - in which each of the n variables...

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