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Numerical · Q38

Q.Draw the symbol and write the truth table and Boolean expression of a two-input NAND gate, and show how a NAND gate can, by itself, be used to realise a NOT gate.

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A NAND gate's symbol is the AND-gate symbol with a small inversion bubble added at its output. Its truth table is the row-for-row complement of the AND gate's own table: output Y=0Y=0 only in the single row where A=1A=1 and B=1B=1, and Y=1Y=1 in every other row. Its Boolean equation is Y=A⋅B‾Y=\overline{A\cdot B}. To realise a NOT gate from a NAND gate ALONE, connect BOTH of its inputs to the same single signal AA: the gate then sees AA on both inputs, so Y=A⋅A‾=A‾Y=\overline{A\cdot A}=\overline{A}, exactly the NOT-gate function. …

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