Boolean logic

• A security light system has two sensors: L (for light level) and M (for movement). The light should turn on (Output O) if it is dark AND there is movement, OR if there is movement AND the user has manually overridden the system (Input R). Assume 1 = true/on, 0 = false/off. a) Construct a Boolean expression for Output O using inputs L, M, and R. b) Complete the truth table for this security light system. Include columns for any intermediate values if helpful. | L | M | R | (L' AND M) | (M AND R) | O | |---|---|---|------------|-----------|---| | 0 | 0 | 0 | | | | | 0 | 0 | 1 | | | | | 0 | 1 | 0 | | | | | 0 | 1 | 1 | | | | | 1 | 0 | 0 | | | | | 1 | 0 | 1 | | | | | 1 | 1 | 0 | | | | | 1 | 1 | 1 | | | | [8 marks]
• Which of the following best describes the purpose of a truth table?
• A digital alarm system uses two sensors, S1 and S2. The alarm (A) sounds if both S1 and S2 detect an intrusion. If only S1 detects an intrusion, the alarm does not sound. If only S2 detects an intrusion, the alarm does not sound. If neither detects an intrusion, the alarm does not sound. a) Complete the truth table for this alarm system. | S1 | S2 | A | |----|----|---| | 0 | 0 | | | 0 | 1 | | | 1 | 0 | | | 1 | 1 | | b) Draw the logic gate diagram for this alarm system. Clearly label inputs S1 and S2, and output A. [4 marks]

Objectives are grouped by subtopic so students can jump straight to the exact skill they want to revise.