Functional Completeness - Examples

Examples

  • Examples of using the NAND completeness. As illustrated by,
    • ¬A = A NAND A
    • A ∧ B = (A NAND B) NAND (A NAND B)
    • A ∨ B = (A NAND A) NAND (B NAND B)
  • Examples of using the NOR completeness. As illustrated by,
    • ¬A = A NOR A
    • A ∧ B = (A NOR A) NOR (B NOR B)
    • A ∨ B = (A NOR B) NOR (A NOR B)

Note that, an electronic circuit or a software function is optimized by the reuse, that reduce the number of gates. For instance, the "A ∧ B" operation, when expressed by NAND gates, is implemented with the reuse of "A NAND B",

X = (A NAND B); A ∧ B = X NAND X

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