Find the boolean expression for the logic circuit, Computer Engineering

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Find the boolean expression for the logic circuit shown below.

2053_Find the boolean expression for the logic circuit.png

Ans. Output of Gate-1 (NAND) = (AB)'

Output of Gate-2 (NOR) = (A'+B)'
Output of Gate-3 (NOR) = [(AB)' + (A'+B)']'

Here applying the De-Morgans law, (X+Y)' = X'Y'
and (XY)' = (X'+Y') [(AB)' + (A'+B)']' = [(AB)']' [(A'+B)']'
= (AB) (A'+B)
= AA'B + ABB
= ABB
= AB.

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