Question Details

Which is correct truth table for given circuit?

Options

A

A B Z
0 0 1
0 1 1
1 0 1
1 1 0

B

A B Z
0 0 0
0 1 1
1 0 1
1 1 0

C

A B Z
0 0 0
0 1 0
1 0 0
1 1 1

D

A B Z
0 0 0
0 1 1
1 0 0
1 1 1

Correct Answer :

A B Z
0 0 0
0 1 1
1 0 1
1 1 0

Solution :

The correct truth table for the given circuit is:

A B Z
0 0 0
0 1 1
1 0 1
1 1 0

Step-by-Step Analysis of the Logic Circuit:

1. Identify the Logic Gates and Connections:
- The circuit has two inputs labeled A and B on the left.
- There are two AND gates in the middle.
- There are two NOT gates (inverters) connected to the input branch lines.
- The final gate on the right is an OR (or XOR) gate producing output Z.

2. Determine the Output of the Top AND Gate:
- One input is taken directly from the input wire of A.
- The other input is taken from the input wire of B and passed through a NOT gate. Therefore, this input is B¯ (NOT B).
- Thus, the output of the top AND gate is:
Y1=A·B¯

3. Determine the Output of the Bottom AND Gate:
- One input is taken from the input wire of A and passed through a NOT gate, resulting in A¯ (NOT A).
- The other input is taken directly from the input wire of B.
- Thus, the output of the bottom AND gate is:
Y2=A¯·B

4. Find the Final Output Function (Z):
- The final gate combines the two outputs Y1 and Y2.
- Assuming an OR gate at the end, the output expression is:
Z=Y1+Y2=(A·B¯)+(A¯·B)
- This expression represents the standard logic formula for a 2-input XOR (Exclusive OR) gate:
Z=AB

5. Construct the Truth Table:
- Let's evaluate the output Z for all possible combinations of inputs:
- If A=0 and B=0:
Z=(0·1)+(1·0)=0+0=0
- If A=0 and B=1:
Z=(0·0)+(1·1)=0+1=1
- If A=1 and B=0:
Z=(1·1)+(0·0)=1+0=1
- If A=1 and B=1:
Z=(1·0)+(0·1)=0+0=0

Unlock Our Free Library

Access expert-curated educational resources and study materials—completely free.

Discover more resources

You may also like

Mock Tests

View All
  • JEE
  • intermediate
  • 3 hours
  • chemistry, mathematics, physics

  • JEE
  • intermediate
  • 3 hours
  • chemical engineering, mathematics, physics