9/18/08
ESE218 Fall 2008 Lecture 6
1
ESE218 Lecture 6.
Standard forms. Twolevel implementations
Outline
Standard forms
SOP and POS, form conversion
Canonical standard forms
minterms, sum of minterms
Maxterms, products of maxterms
form conversion
Implementations of algebraic expressions
ANDOR vs NANDNAND
ORAND vs NORNOR
Opendrain, threestate and wired logic
AOI and OAI
Summary
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9/18/08
ESE218 Fall 2008 Lecture 6
2
Canonical standard forms
SOP:
F = ABD + C’D =
ABD(C+C’)+(A+A’)(B+B’)C’D =
=
ABCD+ABC’D+ABC’D+A’BC’D+AB’C’D+A’B’C’D
1
POS:
F = (A+C’)(B+C’)D =
(A+BB’+C’+DD’)(AA’+B+C’+DD’)(AA’+BB’+CC’+D) =
= (A+B+C’+DD’)(A+B’+C’+DD’)(...)(...) =
= (A+B+C’+D) (A+B+C’+D’) (A+B+C’+D) (A+B’+C’+D’)(…)(…)
0
Canonical SOP is a sum of input combinations when function = 1
Canonical POS is a product of input combinations when function = 0
Simplification of an algebraic expression (combination of different terms) begins with
presenting the expression in a canonical form as a sum of smallest pieces, i.e. cases when function
=1
for the SOP form (or when function = 0 for the POS form)
9/18/08
ESE218 Fall 2008 Lecture 6
3
minterms
and
Maxterms
7
6
5
4
3
2
1
0
#
M
7
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 Fall '08
 DONETSKY
 pullup resistor, minterms, Minterms Maxterms, Canonical standard forms

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