CS251 - Computer Organization and Design - Spring 2008

Lecture 3 - Digital Logic


Practical Details

  1. Office hours
  2. Textbook chapter on CD: Appendix B

Digital Logic

The Magic of Digital

The operational amplifier

The Magic of Logic

Whitehead and Russell

Many subsequent alternate formulations

Combinational Logic

Boolean Logic

Laws of thought, discovered/created/formalized by George Boole

AND is the easiest to understand: OR, NOT harder

NOT and either AND or OR is enough to produce any Boolean expression

Rules of Boolean Algebra

TRUE = 1; FALSE = 0.

  1. Excluded middle: NOT NOT X = X
  2. Identity: X + 0 = X; X1 = X
  3. Zero/one: X + 1 = 1; X0 = 0
  4. Idempotence: X+X = X; XX = X
  5. Inverse: X + NOT X = 1; (NOT X)X = 0
  6. Commutativity: X + Y = Y + X; XY = YX
  7. Associativity: (X + Y) + Z = X + (Y + Z); (XY)Z = X(YZ)
  8. Distribution: X(Y + Z) = XY + XZ; X + YZ = (X + Y)(X + Z)
  9. DeMorgan: NOT ( X + Y) = (NOT X)(NOT Y); NOT (XY) = (NOT X) + (NOT Y)

Connection to Abstract Algebra

XOR can stand in for NOT

Rules of logic are the same as the algebra of Z_2

Truth Tables

Normal Forms

Disjunctive

Conjunctive

Pictures of Gates

Transistors


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