What is the output expression for the circuit shown above?

Answer Details

Okay, let's break down the logic circuit to find the output expression for X.

1. Input A: Goes through a NOT gate. The output of the NOT gate is A' (NOT A).
2. Top AND gate: Takes A' and B as inputs. The output of this AND gate is A' ⋅ B (A' AND B).
3. Bottom AND gate: Takes B and C as inputs. The output of this AND gate is B ⋅ C (B AND C).
4. OR gate: Takes the outputs of the two AND gates (A' ⋅ B and B ⋅ C) as inputs. The output of the OR gate is the sum of its inputs.

Therefore, the final output expression for X is:

X = (A' ⋅ B) + (B ⋅ C)

Or, using alternative notation:

• X = (¬A ∧ B) ∨ (B ∧ C)
• X = (A̅B) + (BC)