Truth tables to solve problems

Applying logical operators in truth tables to solve problems

2.4.1 Boolean Logic

Boolean Logic — Note 4 of 4

What you need to know

Boolean logic can be applied to real-world scenarios by converting conditions into logic gates and truth tables. For example, a security system might grant access only when a keycard AND a PIN are provided. You need to be able to design truth tables and logic circuits for given scenarios, and determine outputs for specific input combinations.

What to know

Real-world problems can be modelled using Boolean logic and truth tables.
Identify the inputs (conditions) and the desired output for the scenario.
Watch for NOT conditions in the scenario: 'nighttime' when the sensor input is 'daytime' means NOT B.
Choose appropriate gates (AND, OR, NOT) to produce the correct output.
Build the truth table showing all possible input combinations and the resulting output.
Draw the corresponding logic circuit diagram using standard gate symbols.

Exam technique

Tip:Read the scenario carefully for hidden NOT conditions. 'Not valid on Saturdays' means NOT C. 'At nighttime' when sensor measures daylight means NOT B.

Example:Floodlight on when switch ON (C) AND motion detected (A) AND nighttime (NOT B, since B=daytime). Q = A AND NOT B AND C — needs NOT gate on B and two AND gates.
Example:Cinema: customer 15+ (A) AND (has ticket (B) OR has money (C)). P = A AND (B OR C).
Example:Restaurant: half-price if (student (A) OR discount card (B)) AND NOT Saturday (C). P = (A OR B) AND NOT C.

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