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The psi operator is a 3-digit switching function . Its special meaning is that every switching function can be represented by the psi operator.
Table of values of the psi operator
The psi operator is defined by the following table of values:
a
b
c
Ψ (a, b, c)
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
This corresponds to .
Representation of any switching functions by the psi operator
sentence
Any switching function can be represented by the psi operator.
Proof (sketch)
It suffices to show that the three functions logical negation , logical and and logical or can be represented. This can be achieved through suitable inputs for the psi operator.
