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NAND, NOR, and EXOR (more primitive logical gates)

NAND, NOR, and EXOR (more primitive logical gates). CS 147 - Computer Architecture David Mayer. Uses for NAND, NOR, and EXOR gates. Control systems, such as for air conditioning and automobiles. Circuit boards, for on-board logic. Internally, in more complex integrated circuit chips.

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NAND, NOR, and EXOR (more primitive logical gates)

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  1. NAND, NOR, and EXOR(more primitive logical gates) CS 147 - Computer Architecture David Mayer

  2. Uses for NAND, NOR, and EXOR gates • Control systems, such as for air conditioning and automobiles. • Circuit boards, for on-board logic. • Internally, in more complex integrated circuit chips.

  3. NAND = Negated AND TRUE iff any of its inputs are FALSE Symbols for Logic Diagram

  4. NAND with Karnaugh Map (K-Map) K-Map K-Map

  5. NAND with Algebraic Equation K-Map Q = A•B (or just Q = AB) Algebraic Equation

  6. NAND (all forms) K-Map Q = AB

  7. NOR = Negated OR FALSE iff any of its inputs are TRUE Symbols for Logic Diagram

  8. NOR with K-Map K-Map

  9. NOR with Algebraic Equation Q = A+B Algebraic Equation

  10. NOR (all forms) Q = A+B

  11. EXOR = Exclusive OR(often symbolized XOR) TRUE iff only one of its inputs is TRUE Symbol for Logic Diagram

  12. XOR with K-Map K-Map

  13. Q = A B XOR with Algebraic Equation Algebraic Equation

  14. Q = A B XOR (all forms)

  15. NAND is a universal gate • Can be used to implement all Boolean functions. = = =

  16. More NAND as universal gate = = = =

  17. NOR is also a universal gate = = =

  18. More NOR as universal gate = = = =

  19. The NAND circuit is much simpler to implement than the NOR circuit, and the NAND is a universal gate; so chip manufacturers typically make all their logical devices (primitive or otherwise) out of combinations of NAND gates, to simplify the manufacturing design process.

  20. Questions or comments?

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