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Lecture03

# Lecture03 - ENGRD 2300 Introduction to Digital Logic Design...

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1 ENGRD 2300 Introduction to Digital Logic Design Fall 2009 Boolean Algebra (Switching Algebra) Lecture 3: 1 Announcements HW1 Will be posted soon This assignment is due Wed Sept 16 at 1:25pm, in the Homework Dropbox Lab 1 has been posted on Blackboard Prelab for Lab 1 is due Mon Sept 7 at 1:25pm I’ll post an announcement on Blackboard when CMS is ready Lecture 3: 2 Bring a paper copy of the lab instructions (to be posted soon) to lab with you For next class Read Wakerly 4.2 and make sure you have read (Ch 1, Ch 3.1-3.3, and Ch 4.1)

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2 Switching Algebra Mathematical tool for analyzing and synthesizing logic circuits Boolean algebra Developed by George Boole in 1854 Two-valued algebraic system Used to formulate true or false postulations Switching algebra Claude Shannon, 1938 Lecture 3: 3 Adopted Boolean algebra to analyze behavior of digital circuits 2 values Î LOW/HIGH, off/on, etc. Boolean Algebra Most of the time, we deal with positive logic conventions LOW and HIGH analog voltages map to 0 and 1 There are also negative logic conventions LOW and HIGH analog voltages map to 1 and 0 Signal values are represented by variables Lecture 3: 4 X, Y, Z, Clk, data0, etc.
3 Some Definitions Literal: a variable or its complement X, X’, imageek Expression: literals combined by AND, OR, parentheses, complementation (not) X+Y P • Q • R A + B • C ((urageek • Z’) + A • B’ • C + Q5) • RESET’ Lecture 3: 5 Equation: Variable = expression P = ((wrallgeeks • Z’) + A • B’ • C + Q5) • RESET’ Complement: X’=/X (opposite of X) AND: X • Y OR X+Y binary operators, described functionally by truth tables Boolean operators OR: X + Y Lecture 3: 6

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4 Possible Logic Functions of Two Variables There are 16 possible functions of 2 input variables In general there are 2 2 n functions of n inputs X Y 16 possible functions (F0–F15) 0 00000000011111111 0 10000111100001111 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 X Y F In general, there are 2 Lecture 3: 7 1 10101010101010101 X nor Y not (X or Y) X nand Y not (X and Y) 1 0 X or Y X and Y X xor Y X Y
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Lecture03 - ENGRD 2300 Introduction to Digital Logic Design...

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