Design a simple logic system from a written specification by building its truth table and selecting the gates needed

What this dot point is asking

SEAB wants you to design a simple logic system from a written description, by turning the words into a truth table, then a Boolean expression, then a circuit of gates. The central insight is that a problem stated in plain English ("sound the alarm when this and that, or the other") maps directly onto logic gates, with words like "and", "or" and "not" pointing to the gate you need.

The answer

From words to logic

Designing a logic system follows a fixed route:

1. Identify the inputs and the output. Give each a letter and decide what logic 1 means for each (for example, $D = 1$ when a door is open).
2. Write the truth table. For every input combination, decide from the specification whether the output should be 1 or 0.
3. Write the Boolean expression. Read it from the rows where the output is 1, or directly from the wording.
4. Choose the gates and draw the circuit. Translate the expression into gates, with AND for a dot, OR for a plus and NOT for a bar.

Spotting the gate from the words

The language of the specification points to the gates:

• "A and B" both needed means an AND gate.
• "A or B" either being enough means an OR gate.
• "not A" or "when A is off" means a NOT gate.
• "Sound the alarm unless all is clear" often becomes a NOR gate, since NOR is high only when all inputs are 0.

Building the expression from the truth table

If the wording is complex, build the table first, then read off each row where the output is 1. Each such row contributes a term: an AND of the inputs (inverted where they are 0 in that row), and the terms are joined by OR. This guarantees a correct expression even when the description is awkward.

Overrides and combinations

Real systems often combine conditions. A common pattern is a sensing condition combined with a manual override: $Q = (\text{sensor logic}) + M$, where ORing the override $M$ forces the output on regardless of the sensors. Building from small, clearly named blocks keeps even a multi-input design manageable.

Examples in context

Example 1. A car seatbelt reminder. The chime should sound when the engine is on AND the seatbelt is unfastened. Naming the inputs and writing the two-row-relevant truth table leads straight to $Q = E \cdot \bar{S}$, built from a NOT gate (to invert the fastened signal) feeding an AND gate. A real safety feature falls out of two gates.

Example 2. A pedestrian crossing request. A "wait" light should come on when a button is pressed OR the timer demands a stop, but only while the system is enabled. The wording maps to an OR gate feeding an AND gate with the enable signal. Designing from the specification keeps the logic transparent and easy to test against the requirement.

Try this

• Cue. A pump runs when the tank is empty AND the supply is available. Give the Boolean expression and the gate. $Q = E \cdot S$, built from a single AND gate.

• Cue. An alarm sounds when neither sensor detects all-clear, that is when both sensors read 0. Name the suitable single gate. A NOR gate, which is high only when all inputs are 0.

• Cue. Explain how a manual override is added to a sensor-driven output. OR the override signal onto the sensor logic, so the output is forced on whenever the override is 1, regardless of the sensors.