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  4. The diagram of a logic circuit is given below. The output F of the circuit is represented by

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Q. The diagram of a logic circuit is given below. The output $F$ of the circuit is represented byPhysics Question Image

Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

Output of upper OR gate $=W+X$
Output of lower OR gate $=W+Y$
Net output, $F=(W+X)(W+Y)$
$=W W+W Y+X W+X Y$ (Since $W W=W)$
$=W(1+Y)+X W+X Y$ (Since $1+Y=1$)
$=W+X W+X Y=W(1+X)+X Y=W+X Y$