Unit 2 - ERG 2020A Unit 2 Combinational Logic I Professor...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
1 ERG 2020A Unit 2 Combinational Logic I Professor K.W.Cheung HSH 819 X 8348 kwcheung@ie.cuhk.edu.hk
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Outline • Boolean Algebra • Combinational Logic Analysis • Combinational Logic Synthesis
Background image of page 2
3 Objectives • Use Boolean Algebra to describe digital logic – Formal representation – Pragmatic approach – De-emphasize algebraic reduction and manipulation of Boolean expressions • Learn the techniques for understanding and designing combinational circuits – Standard forms – Optimization of circuit elements (only a minimal understanding of the Karnaugh map technique)
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 What is a combinational circuit? • A digital circuit with all outputs that depend only the “instantaneous” values of the inputs – In reality, there is always some finite delay (propagation and processing) incurred in traversing through a digital circuit – The delay can cause problems (ignore this for the time being) • Has no internal memory, no internal states
Background image of page 4
5 Boolean algebra • a.k.a. “switching algebra” – deals with boolean values -- 0, 1 • Historically, C.Shannon rediscovered G.Boole’s work • Positive-logic convention – analog voltages LOW, HIGH --> 0, 1 • Negative logic -- seldom used • Signal values denoted by variables (X, Y, FRED, etc.)
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 Boolean operators • Complement: X (opposite of X) • AND: X × Y •OR : X + Y • Notations for convenience binary operators, described functionally by truth table.
Background image of page 6
7 Axioms of Switching Algebra • A1 : X = 0 if X 1 A1’ : X = 1 if X 0 • A2 : if X = 0 then X’ = 1 A2’ : if X = 1 then X’ = 0 • A3 : 0.0 = 0 A3’ : 1 + 1 = 1 • A4 : 1.1 = 1 A4’ : 0 + 0 = 0 • A5 : 0.1 = 1.0 = 0.0 A5’ : 1 + 0 = 0 + 1 = 1 • Operator Precedence : NOT > AND > OR
Background image of page 7

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

View Full DocumentRight Arrow Icon
8 More definitions • Literal: a variable or its complement – X, X , FRED , CS_L • Expression: literals combined by AND, OR, parentheses, complementation –X+Y –P × Q × R –A + B × C –( (FRED × Z ) + CS_L × A × B × C + Q5) × RESET • Equation: Variable = expression = ( × Z ) + CS_L × A × B × C + Q5) × RESET
Background image of page 8
9 Logic symbols
Background image of page 9

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

View Full DocumentRight Arrow Icon
10 Theorems • Proofs by perfect induction
Background image of page 10
11 More Theorems • N.B. T8 , T10, T11
Background image of page 11

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

View Full DocumentRight Arrow Icon
12 Proof of T11 RHS X.Y + X’.Z Use T9: RHS => (X+X.Z).Y + (X’+X’.Y).Z => X.Y + X.Y.Z + X’Z + X’.Y.Z => X.Y + X’.Z + (X+X’).Y.Z => LHS Exercise: Try prove T11’
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/18/2010 for the course INFORMATIO IEG 2810AB taught by Professor Professork.w.cheung during the Spring '09 term at CUHK.

Page1 / 57

Unit 2 - ERG 2020A Unit 2 Combinational Logic I Professor...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online