Skip to content
Sahithyan's S2
Sahithyan's S2 — Computer Organization And Digital Design

Logic Circuit Simplification

Digital logic circuits can be simplified using boolean algebra.

Boolean algebra

Axioms

  • Absorption:
  • Absorption #2:

Duality

Dual

For a boolean expression, its “dual” is defined as the boolean expression where:

  • all the are replaced with
  • all the are replaced with
  • all the are replaced with
  • all the are replaced with
  • all variables left intact

When a theorem is proven, also its dual is proven

de Moragan’s theorem

A procedure for complementing boolean functions.

  • all the are replaced with
  • all the are replaced with
  • all the are replaced with
  • all the are replaced with
  • all variables are replaced with their complements

Uniting theorem