Lec3_0119

# Lec3_0119 - 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 L3.1 CS M51A/EE M16 Winter’05 Section 1 Logic Design of Digital Systems Lecture 3 Yutao He [email protected] 4532B Boelter Hall http://courseweb.seas.ucla.edu/classView.php?term=05W&srs=187154200 January 19 W’05

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Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.2 Outline Administrative Matters Recap: Data presentation Chapter 2.4-2.5, App. A Switching Function Switching Expression Switching (Boolean) Algebra Canonical Forms Summary
Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.3 Administrative Matter HW #2 is posted HW #1 Solution is posted Quiz #1 will be held on Friday About Lecture note posting

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Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.4 Review - Data Representation Encode with binary number 0s and 1s Character ASCII Unicode Number (positive integer) Positional Number Systems Context is very important! What’s the output? • int a = 12; printf (“a is %d”, a); What if • char a = ‘2’; printf (“a is %d”, a); How about int a = 12; printf (“a is %x”, a);
Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.5 Review - Code for Decimal Numbers Binary-Coded-Decimal (BCD) Code: Encode each decimal digit individually using binary codes Example: Encode decimal number sixteen (16): Binary Code: 10000 BCD Code: 0001 0110

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Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.6 Binary-Level Specification High-Level Spec F H X H Y H Encoding Decoding Binary-Level Spec F B n m x B y B
Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.7 Truth Table Tabular representation of switching functions x y f x y f 0 0 0 0 1 1 1 0 0 1 1 1 i 0 1 2 3 There are 2^n rows for a n-input switching function

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Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.8 2-D Truth Table
Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.9 Truth Table of 1-Input S. F. x f X f f f f 0 0 0 1 1 1 0 1 0 1 i 0 1 0 1 2 3 0-Constant 1-Constant Identity (Buffer) Complement (NOT)

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Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.10 Truth Table of 2-Input S. F. How many different switching functions can be obtained from a n-input switching function? 2 2 n x y f AND OR XOR NOR EQU NAND x y 16 possible functions (f0–f15) 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.11 Incompletely Specified S. F. Output value is not specified for a given input combination: Don’t care x y z f 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 - 1 0 0 1 1 0 1 0 1 1 0 - 1 1 1 1

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Y. He @ 02/14/11 CSM51A/EEM16-Sec1 W’05 L3.12 One/Zero Set Notations i x y z f 0 0 0 0 0 1 0 0 1 1 2 0 1 0 0 3 0 1 1 - 4 1 0 0 1 5 1 0 1 0 6 1 1 0 - 7 1 1 1 1 One/Zero/D.C. Set Notations: f (x,y,z) = one-set(1,4,7), d.c.-set(3,6) or f(x,y,z) = zero-set(0,2,5), d.c.-set(3,6)
Y. He @ 02/14/11

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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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Lec3_0119 - CS M51A/EE M16 Winter'05 Section 1 Logic Design...

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