Shannon Expansion Explorer

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Description

Explore Shannon's Expansion Theorem, which allows any Boolean function to be decomposed into cofactors. This is the foundation for multiplexer implementation and Binary Decision Diagrams.

Learning Objectives

Bloom Level: Analyze (L4)

After using this MicroSim, students will be able to:

  • ✓ Analyze function decomposition using Shannon expansion
  • ✓ Calculate positive and negative cofactors
  • ✓ Apply expansion to multiplexer implementation

Shannon's Theorem

F = x' · F|x=0 + x · F|x=1

  • ● F|x=0 is the cofactor when x=0 (substitute x=0 in F)
  • ● F|x=1 is the cofactor when x=1 (substitute x=1 in F)

Applications

  1. Multiplexer Implementation: Cofactors become MUX data inputs
  2. BDD Construction: Recursive decomposition builds decision diagrams
  3. FPGA Mapping: Function decomposition for lookup tables

How to Use

  1. Select a Boolean function
  2. Choose which variable to expand on
  3. Observe the cofactors F|x=0 and F|x=1
  4. See the resulting expanded form

References