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Boolean Logic - Secondary Operators

XOR

Also known as the inequality operator since it is true only when its two arguments are not equal. XOR is equivalent to (a AND NOT b) OR (NOT b AND a).

Different XOR operator notation:

  • a != b
  • a XOR b

Truth table for the XOR operator:

aba != b
000
010
100
111

IMPLIES

The use of this operator is known as implication. IMPLIES is equivalent to a' + b.

Different IMPLIES operator notation:

  • a => b
  • a IMPLIES b

Truth table for the IMPLIES operator:

aba => b
001
011
100
111

BI-IMPLIES

BI-IMPLIES is also known as the equivalence operators, and is the inverse of XOR. The use of BI-IMPLES is known as bi-implication. It is the same as (a . b) + (a' . b').

Different BI-IMPLIES operator notation:

  • a <=> b
  • a BIIMPLIES b

Truth table for the BI-IMPLIES operator:

aba <=> b
001
010
100
111

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