218L5S09

# 218L5S09 - ESE218 Lecture 5 Switching algebra Two-level...

This preview shows pages 1–6. Sign up to view the full content.

2/10/09 ESE218 Spring 2009 Lecture 5 1 ESE218 Lecture 5. Switching algebra. Two-level implementations. Standard forms Outline ± Switching algebra ² Positive and negative logic ² Duality principle ² Axioms ² Distributive law ² Theorems ² DeMorgan’s law ± Functionally complete sets ± NAND ± NOR ± XOR and XNOR operations ± Functions of two variables and extension to multiple inputs ± Circuit levels and propagation delay ± Standard forms ² sum of products ² products of sums ² form conversion ± Summary

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

View Full Document
2/10/09 ESE218 Spring 2009 Lecture 5 2 Switching algebra Claude Elwood Shannon 1916-2001 B = { 0, 1 } (X) OR (Y) = X + Y (X) AND (Y) = X Y NOT (X) = X’
2/10/09 ESE218 Spring 2009 Lecture 5 3 Positive and negative logic +5 +5 +5 +5 GND +5 +5 +5 GND GND GND GND F Y X GND = 0 +5 = 1 GND = 1 +5 = 0 1 1 1 1 0 1 1 1 0 0 0 0 F Y X 0 0 0 0 1 0 0 0 1 1 1 1 F Y X F = X + Y F = X Y Assuming positive logic Assuming negative logic V1 5Vdc 1k R1 0 4 3 1 2 4 3 1 2 F Y X

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

View Full Document
2/10/09 ESE218 Spring 2009 Lecture 5 4 Duality principle Every algebraic expression remains valid if (1) operators “+” and “ (2) identity elements “0” and “1” are interchanged: Change 0 1 1 0 + →⋅ ⋅→ + Valid Expression (X + 1) 0 = 0 Valid Expression X 0 + 1 = 1 Keep the original order of operations!
2/10/09 ESE218 Spring 2009 Lecture 5 5 Functionally complete sets 5 6 4 U4B 7402 4 5 6 U3B 7400 1 2 3 U1A 7400 F = (X+Y)’ X Y F = (XY)’ X Y X 4 5 6 U1B 7400 9 10 8 U1C

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.

{[ snackBarMessage ]}

### Page1 / 16

218L5S09 - ESE218 Lecture 5 Switching algebra Two-level...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online