In the truth table of the above circuit the value of $$X$$ and $$Y$$ are :

To find the values of X and Y in the truth table, we need to trace the logic circuit step-by-step for each of the given input combinations.

1. Identify the Logic Gates

The circuit consists of the following components:

• Top Gate: An AND gate with inputs A and B. Its output is $$A \cdot B$$.
• Bottom Path: Both inputs A and B pass through individual NOT gates (inverters) before entering a second AND gate. Its output is $$\overline{A} \cdot \overline{B}$$.
• Output Gate: A NOR gate that takes the outputs from both paths. Its final output equation for E is:
• Top AND Gate: $$0 \cdot 1 = 0$$
• Bottom Path: * Inverting the inputs gives $$\overline{0} = 1$$ and $$\overline{1} = 0$$.
  • The bottom AND gate receives these inverted inputs: $$1 \cdot 0 = 0$$.
• Final NOR Gate: It receives 0 and 0 as inputs.
  • OR operation: 0 + 0 = 0
• NOT operation (inversion): $$\overline{0} = 1$$
• Top AND Gate: $$1 \cdot 0 = 0$$
• Bottom Path: * Inverting the inputs gives $$\overline{1} = 0$$ and $$\overline{0} = 1$$.
  • The bottom AND gate receives these inverted inputs: $$0 \cdot 1 = 0$$.
• Final NOR Gate: Just like the previous case, it receives 0 and 0 as inputs.
  • OR operation: 0 + 0 = 0
• NOT operation (inversion): $$\overline{0} = 1$$

$$E = \overline{(A \cdot B) + (\overline{A} \cdot \overline{B})}$$

2. Finding the Value of X (Inputs: A = 0, B = 1)

Let's substitute these inputs into the circuit paths:

Therefore, X = 1.

3. Finding the Value of Y (Inputs: A = 1, B = 0)

Let's substitute these inputs into the circuit paths:

Therefore, Y = 1.

Final Truth Table Summary

$$\boxed{X = 1 \quad \text{and} \quad Y = 1}$$