A car's warning light system uses the following logic: The warning light comes on if the fuel level is low OR the engine temperature is high The light also ...

(a) Boolean expression for the warning light W: [3]

W = (F OR T) OR (D AND M)

[1] for F OR T (fuel low or temperature high), [1] for D AND M (door open and car moving), [1] for combining both with OR.

The warning light activates if either condition is met: a fuel/temperature problem, or a door-while-moving situation. The OR at the top level means satisfying either sub-condition is enough.

(b) Completed truth table: [3]

[1] for F OR T column correct, [1] for D AND M column correct, [1] for W column correct.

Row 1: no problems, W=0. Row 2: fuel low, W=1. Row 3: door open while moving, W=1. Row 4: engine hot (temperature), W=1. Row 5: all problems present, W=1.

(c) When fuel is not low (F=0), temperature is normal (T=0), door is open (D=1), car is stationary (M=0): [2]

W = (0 OR 0) OR (1 AND 0) = 0 OR 0 = 0

The warning light is OFF. [1] Neither condition is triggered: fuel and temperature are fine, and although the door is open, the car is not moving so D AND M = 0. [1]

(d) Number of logic gates needed: 3 gates [1]

• 1 OR gate for F OR T
• 1 AND gate for D AND M
• 1 OR gate to combine both results into W [1]

(e) The output expression for the described circuit is: Z = (A AND B) OR (NOT C) [1 for correct operators, 1 for correct structure].

(f) Truth table where the output is 1 when at least two inputs are 1: [3]

[1] for rows where output is 0 (fewer than two 1s), [1] for rows with exactly two 1s giving output 1, [1] for the row with all three 1s also giving output 1. This is known as a majority function.