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

Question

The diagram of a logic circuit is given below. The output F of the circuit is represented by (A) W ⋅(X+Y) (B) W ⋅(X ⋅ Y) (C) W+(X ⋅ Y) (D) W+(X+Y)

Tardigrade Admin · Accepted Answer

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

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

$W \cdot (X + Y)$

$W \cdot (X \cdot Y)$

$W + (X \cdot Y)$

$W + (X + Y)$

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

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

W⋅(X+Y)

W⋅(X⋅Y)

W+(X⋅Y)

W+(X+Y)