PPT Slide

2 – Combinational Logic

© 1996 Gaetano Borriello

The uniting theorem

• Key tool to simplification: A (B' + B) = A

• Essence of simplification of two-level logic

  • find two element subsets of the ON-set where only one variable changes its value – this single varying variable can be eliminated and a single product term used to represent both elements

37

A B F

0 0 1

0 1 0

1 0 1

1 1 0

B has the same value in both on-set rows– B remains

A has a different value in the two rows– A is eliminated

F = A'B'+AB' = (A'+A)B' = B'

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