Question

A logic circuit provides the output y as per the following truth table:

A	B	Y
0	0	1
0	1	0
1	0	1
1	1	0

The expression for the output Y is:

• A. \(A.B+\overline A\)
• B. \(A.\overline B+\overline A\)
• C. \(\overline B\)
• D. \(B\)

Answer 1

The Correct Option is C

To find the expression for the output Y, we analyze the truth table:

A	B	Y
0	0	1
0	1	0
1	0	1
1	1	0

We look for the rows where Y is 1:

- When A=0 and B=0, Y=1.
- When A=1 and B=0, Y=1.

From the first row, we have A'B' (where A' and B' represent the complements of A and B, respectively).

From the third row, we have AB'.

Therefore, the expression for Y is the sum of these two terms:

Y = A'B' + AB'

We can simplify this expression:

Y = B'(A' + A)

Since A' + A = 1, we have:

Y = B' * 1

Y = B'

So, the expression for the output Y is B'.

Final Answer:

B'

Answer 2

The truth table provided gives the values for \(A\), \(B\), and \(Y\). To find the expression for \(Y\), consider the outputs:

A	B	Y
0	0	1
0	1	0
1	0	1
1	1	0

The output \(Y\) is 1 for the combinations where \(B=0\) (either \(A=0, B=0\) or \(A=1, B=0\)). This indicates the condition \(Y = \overline{B}\). Therefore, the correct expression for the output based on the truth table is \(\overline{B}\), which matches the option \(\overline{B}\).