Lec6_0131

# Lec6_0131 - CS M51A/EE M16 Winter'05 Section 1 Logic Design...

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Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W’05 L6.1 CS M51A/EE M16 Winter’05 Section 1 Logic Design of Digital Systems Lecture 6 Yutao He [email protected] 4532B Boelter Hall http://courseweb.seas.ucla.edu/classView.php?term=05W&srs=187154200 January 31 W’05

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Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W’05 L6.2 Outline Administrative Matters Recap Minimization with K-Map using implicants and friends Chapter 5 Minimization with K-Map using implicates and friends Minimization with Quine-McCluskey algorithm Transformation between different types of gate networks Summary
Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W’05 L6.3 Administrative Matters Quiz #1 Solution is posted Homework #4 Is posted and due on Feb. 7 Quiz #2 Will be given on Friday Wednesday’s Lecture Will cover Ch. 6 not Ch. 4

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Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W’05 L6.4 Basic structure: Difference with 2-D function table? Basic condition: Adjacency condition Basic concepts: Implicants, prime implicants, and essential prime implicants Basic skills: Obtain K-Map of a switching function Minimization of a two-level network with K-Map Karnaugh Map - Review
Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W’05 L6.5 Review - Minimization w/ K-Map x’ 3 x’ 2 x’ 0 , x’ 2 x’ 1 x’ 0 , x 2 x 0, x 3 x’ 1 x 2 x 0 x 1 12 13 15 14 8 9 11 10 0 1 3 2 4 5 7 6 x 3 1 0 0 1 - 1 1 0 1 - 1 1 1 - 0 0 Primary implicants: x’ 2 x’ 1 x’ 0 x’ 3 x’ 2 x’ 0 x 2 x 0 x 3 x’ 1 Essential primary implicants: x 2 x 0, x 3 x’ 1, x’ 3 x’ 2 x’ 0 Minimal Switching Expression: F(x 3, x 2, x 1 , x 0 ) = x 2 x 0 + x 3 x’ 1 + x’ 3 x’ 2 x’ 0 The minimal switching expression is unique!

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Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W’05 L6.6 Sum Terms and K-Map 00 01 11 10 x 3 x 2 x 1 x 0 11 10 12 13 15 14 8 9 11 10 00 01 0 1 3 2 4 5 7 6 0 1 1 0 1 0 1 1 0 0 0 0 1 1 - - Maxterm M i corresponds to 0-cell with label i . A sum (OR) term of n-1 literals corresponds to a rectangle composed of 2 adjacent 0-cells. A sum (OR) term of n-j literals corresponds to a rectangle composed of 2 j adjacent 0-cells. M 0 x’ 3 + x 2 + x 1 x’ 2 + x’ 0
Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W’05 L6.7 Minimization - Concepts Implicate A sum term that a function equals to 0 whenever it equals to 0 for a given assignment.

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## This note was uploaded on 02/14/2011 for the course CS M51A taught by Professor Ercegovac during the Winter '07 term at UCLA.

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Lec6_0131 - CS M51A/EE M16 Winter'05 Section 1 Logic Design...

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