Question 19

The correct truth table for the following logic circuit is :

Name: The correct truth table for the following logic circuit is :
Uploaded: 2026-05-20T11:08:36.269015+05:30
Duration: 1 min 52 s
Description: The correct truth table for the following logic circuit is :

Solution

$$\text{Top input} = \bar{A} \quad (\text{via NOT gate})$$

$$\text{Bottom input} = A \cdot B \quad (\text{via AND gate})$$

$$Y = \bar{A} + (A \cdot B)$$

Using the distributive law of Boolean algebra ($$X + (\bar{X} \cdot Y) = X + Y$$):

$$Y = (\bar{A} + A) \cdot (\bar{A} + B)$$

$$\implies Y = 1 \cdot (\bar{A} + B) = \bar{A} + B$$

For $$A=0, B=0 \implies Y = \bar{0} + 0 = 1 + 0 = 1$$

For $$A=0, B=1 \implies Y = \bar{0} + 1 = 1 + 1 = 1$$

For $$A=1, B=0 \implies Y = \bar{1} + 0 = 0 + 0 = 0$$

For $$A=1, B=1 \implies Y = \bar{1} + 1 = 0 + 1 = 1$$

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The correct truth table for the following logic circuit is :

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