What is the output expression for the circuit shown above?

This question tests the ability to derive a Boolean output expression from a combinational logic circuit built from standard gates.

The circuit contains three inputs: A, B, and C. Two AND gates are present. The first AND gate receives inputs A and B, producing the product AB. The second AND gate receives inputs B and C, producing the product BC. The outputs of both AND gates are then fed into a single OR gate, which combines them to produce the final output.

Applying the rules of Boolean algebra to this arrangement:

• First AND gate output: \( A \cdot B = AB \)
• Second AND gate output: \( B \cdot C = BC \)
• OR gate combines both: \( AB + BC \)

The overall output expression is therefore \( AB + BC \). This is a sum-of-products (SOP) expression, where each AND gate produces a product term and the OR gate sums them.

This expression can also be factored as \( B(A + C) \), showing that the output is HIGH whenever B is HIGH and at least one of A or C is also HIGH. However, the unfactored SOP form AB + BC directly mirrors the gate-level structure of the circuit.

When reading output expressions from logic circuits, trace each path from the inputs through every gate to the final output. AND gates multiply their inputs (product), OR gates add them (sum), and NOT gates invert (complement). The final expression reflects the exact gate arrangement.