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Boolean logic

NOT, AND, OR, NAND, NOR and XOR – symbols and truth tables.

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Logic gates

NOT, AND, OR, NAND, NOR and XOR – symbols and truth tables.

Logic circuits

Construct logic circuits from expressions or problem statements, and complete truth tables for circuits with up to three inputs.

Worked example: Write the truth table outputs for X = (A AND B) OR (NOT C).

X = 1 when A and B are both 1, or when C = 0.

Rows (A B C → X): 000 → 1; 001 → 0; 010 → 1; 011 → 0; 100 → 1; 101 → 0; 110 → 1; 111 → 1

Logic expressions from problems

Worked example: An alarm (X) sounds if the door is open (D = 1) AND the system is armed (S = 1), OR if the panic button is pressed (P = 1).

X = (D AND S) OR P

Applications

Safety systems, control systems and decision-making circuits.

Exam tip: Work column by column in truth tables – evaluate intermediate expressions first.

Check yourself

  1. What is the output of NAND when both inputs are 1?
  2. For XOR, when is the output 1?
  3. How many rows are needed in a truth table with three inputs?
Show answers
  1. 0
  2. When the inputs are different.
  3. 8
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