Lecture03

# Lecture03 - Lecture 3 Spring 2010 1 ECE 2300 Introduction...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 3: Spring 2010 1 ECE 2300 Introduction to Digital Logic Design Switching Algebra Lecture 3: 2 Announcements • HW 1 due this Wednesday at noon – In the HW drop box • Lab 1 is on Blackboard – Prelab is due this Friday at noon – Electronic submission (details in lab write-up) • Instructor and TA office hours are on Blackboard Lecture 3: 3 Switching Algebra • Mathematical tool for analyzing logic circuits • Based on Boolean algebra (George Boole, 1854) – Two-valued algebraic system – Used to formulate true or false postulations • Switching algebra (Claude Shannon, 1938) – Adopted Boolean algebra for digital circuits Lecture 3: 4 Definitions • Literal : a variable or its complement – X, X’, val • Expression : literals combined by AND, OR, complementation (not), parentheses – P • Q • R – A + B • C – ((V • Z’) + A • B’ • C + Q5) • RESET’ • Equation : Variable = expression – P = ((V • Z’) + A • B’ • C + Q5) • RESET’ Lecture 3: 5 • Complement: X’ • AND: X • Y • OR: X + Y Boolean operators Lecture 3: 6 Axioms of Switching Algebra • Axioms come in pairs – Interchange 1 and 0, AND and OR • First axiom: Digital abstraction – A variable X can only take on 2 values (A1) X = 0 if X ! 1 (A1’) X = 1 if X ! Lecture 3: 7 X Y = X’ Other complement symbols: ~X, /X, X Axioms of Switching Algebra • Complement (A2) If X = 0, then X’ = 1 (A2’) If X = 1, then X’ = 0 Lecture 3: 8 • Formal definitions of AND and OR (A3) 0•0=0 (A3’) 1+1=1 (A4) 1•1=1 (A4’) 0+0=0 (A5) 0•1=1•0=0 (A5’) 1+0=0+1=1 • A1-A5 completely define switching algebra – Everything else can be derived from these axioms Axioms of Switching Algebra Lecture 3: 9 Operator Precedence • What does W•X+Y•Z mean? – W•((X+Y)•Z) ? – (W•(X+Y))•Z ? – (W•X)+(Y•Z) ? • As in normal arithmetic, “multiplication” (AND) has precedence over “addition” (OR) – (W•X) + (Y•Z) – Can use parentheses to avoid ambiguity Lecture 3:10 Single-Variable Theorems • Identities: (T1) X+0=X (T1’) X•1=X • Null Elements: (T2) X+1=1 (T2’) X•0=0...
View Full Document

## This note was uploaded on 04/10/2010 for the course ECE 2300 taught by Professor Long during the Spring '08 term at Cornell.

### Page1 / 4

Lecture03 - Lecture 3 Spring 2010 1 ECE 2300 Introduction...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online