What is the output expression for the circuit shown above?

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)