PPT Slide

2 – Combinational Logic

© 1996 Gaetano Borriello

Incompletely specified functions

• Functions of n inputs have 2n possible input configurations

  • for a given function, not all input combinations may be possible
  • this can be exploited during circuit minimization

• Example: binary coded decimal increment by 1

34

A B C D W X Y Z0 0 0 0 0 0 0 1

0 0 0 1 0 0 1 0

0 0 1 0 0 0 1 1

0 0 1 1 0 1 0 0

0 1 0 0 0 1 0 1

0 1 0 1 0 1 1 0

0 1 1 0 0 1 1 1

0 1 1 1 1 0 0 0

1 0 0 0 1 0 0 1

1 0 0 1 0 0 0 0

1 0 1 0 X X X X

1 0 1 1 X X X X

1 1 0 0 X X X X

1 1 0 1 X X X X

1 1 1 0 X X X X

1 1 1 1 X X X X

BCD digits encode the decimal digits0 – 9 in the bit patterns0000 – 1001

off-set of W

on-set of W

don't care (DC) set of W

these inputs patterns should never be encountered in practice – "don't care" about associated output values

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