Possible logic functions of two variables

2 – Combinational Logic

© 1996 Gaetano Borriello

• There are 16 possible functions of 2 input variables:

  • in general, there are 2**(2**n) functions of n inputs

2

X Y 16 possible functions (F0–F15)0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 10 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

0

X and Y

X

Y

X or Y

not Y

not X

1

X

Y

F

X ? Y

X nor Ynot (X or Y)

X = Y

X nand Ynot (X and Y)

as you can see 0, 1, X, X', Y, Y', X • Y, X + Y are only half of the possible functions

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