Question

The output Y of the given logic circuit is

• A. \(\overline{(A\cdot B)}+\overline{(C\cdot B)}\)
• B. \(\overline{(A+B)}\cdot \overline{(B\cdot C)}\)
• C. \(\overline{(A\cdot B)}+\overline{(B+C)}\)
• D. \((A+B)+(B+C)\)

Hint:

Read the figure gate by gate: a NAND of A and B, a NOR of B and C, and an OR of the two outputs.

Answer 1

The Correct Option is C

Step 1: Name the gates by their symbols:
A flat-backed D shape with a bubble is NAND. A curved-back shape with a bubble is NOR. A curved-back shape without a bubble is OR.

Step 2: Follow the wires:
Inputs A and B go into the NAND. Input B (again) and input C go into the NOR. The two outputs join at the OR.

Step 3: Write the expression:
$Y = \overline{AB} + \overline{B+C}$.

Step 4: Match:
Only option (C) contains a NAND of $A, B$ and a NOR of $B, C$ joined by OR.

Final Answer:
Option (C). \[ \boxed{\overline{A\cdot B}+\overline{B+C} \text{ (C)}} \]