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What is the Boolean expression for a 2-input NAND gate?
A + B
A ├ЧB
(\overline{A ├ЧB})
\overline{A + B}
(\overline{A ├ЧB})
A NAND gate is a universal logic gate that performs the inverse of the AND operation. Its Boolean expression is defined as the complement of the AND product of its inputs, A and B.
IEEE Std 91-1984: IEEE Standard Graphic Symbols for Logic Functions
A NAND gate is a universal logic gate that performs the inverse of the AND operation. Its Boolean expression is defined as the complement of the AND product of its inputs, A and B.
Y=AтЛЕB тАФ Boolean algebraic representation of a 2-input NAND gate
AтЛЕB=A+B тАФ DeMorgan's Law equivalent
The NAND gate functions by passing the inputs A and B through an AND operation followed by a NOT operation. The AND operation outputs a high state (1) only if both inputs are high, while the subsequent inversion results in a low state (0) for that specific condition, making the output Y=AтЛЕB.
NAND is a universal gate because any Boolean function can be implemented using only NAND gates.
The truth table of a NAND gate outputs 0 only when all inputs are 1.
The NAND gate is the complement of the AND gate.
In CMOS technology, a NAND gate is physically implemented using series-connected PMOS transistors in the pull-up network and parallel-connected NMOS transistors in the pull-down network.
Universal logic gate capability
Low component count for realization of other logic functions
Increased propagation delay if multiple gates are cascaded
Inversion logic may complicate manual boolean simplification for non-expert designers
Design of digital processors
Implementation of combinational and sequential circuits like flip-flops and multiplexers
Option A (A+B) represents an OR gate.
Option B (A├ЧB) represents an AND gate.
Option D (A+BтАЛ) represents a NOR gate using De Morgan's theorem.
C is correct тАФ the expression (\overline{A ├ЧB}) represents the output of a NAND gate as the inverted product of inputs A and B.
Remember that NAND and NOR are universal gates; always check the inversion bar (complement) over the entire product or sum term when identifying them.
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