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

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

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

NAND with Algebraic Equation K-Map Q = AB (or just Q = AB) Algebraic Equation

NAND (all forms) K-Map Q = AB

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

NOR with K-Map K-Map

NOR with Algebraic Equation Q = A+B Algebraic Equation

NOR (all forms) Q = A+B

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

XOR with K-Map K-Map

XOR with Algebraic Equation Algebraic Equation Q = A B

XOR (all forms) Q = A B

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

More NAND as universal gate == ==

NOR is also a universal gate == =

More NOR as universal gate == ==

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.

Questions or comments?