Define and understand the functions of logic gates

Boolean Logic – IGCSE 0478 (Topic 10)

1. What is Boolean Logic?

• Boolean logic works with **two values only**: 1 (true) and 0 (false).
• It is the language used to describe the behaviour of digital circuits.
• The three fundamental Boolean operators are:
  • AND – output 1 only when all inputs are 1.
  • OR – output 1 when any input is 1.
  • NOT – inverts a single input (1 → 0, 0 → 1).

2. Standard Gate Symbols (Cambridge‑approved)

All symbols are drawn exactly as they appear in the Cambridge exam papers.

Quick‑reference cheat‑sheet (black‑and‑white)

Copy the third column of the table above into your notebook – it contains the exact line‑art symbols you may need during the exam.

3. Truth Tables & One‑Sentence Take‑aways

AND Gate

Take‑away: AND = 1 only when *all* inputs are 1.

OR Gate

Take‑away: OR = 1 when *any* input is 1.

NOT Gate (Inverter)

Take‑away: NOT flips the input (0↔1).

NAND Gate

Take‑away: NAND = inverse of AND; it is 0 only when *all* inputs are 1.

NOR Gate

Take‑away: NOR = inverse of OR; it is 1 only when *all* inputs are 0.

XOR Gate (Exclusive OR)

Take‑away: XOR = 1 when the two inputs are **different**.

XNOR Gate (Exclusive NOR)

Take‑away: XNOR = 1 when the two inputs are **the same** (the complement of XOR).

4. Compare & Contrast – Gate & Its Inverse

5. Building Logic Circuits from Different Sources

Example 1 – From an English problem statement

Problem: “A security system should give an alarm (output = 1) if the door is open and the motion sensor detects movement, or if the window is broken.”

1. Identify the variables
   • D = door open (1 = open, 0 = closed)
   • M = motion detected (1 = motion, 0 = none)
   • W = window broken (1 = broken, 0 = intact)
2. Write the Boolean expression

   Alarm = (D AND M) OR W

3. Draw the circuit (using Cambridge symbols)

   Explanation:

   • The two inputs D and M feed an AND gate.
   • The output of the AND gate and the W input go into an OR gate.
   • The OR gate’s output is the alarm signal.
4. Truth table (derived from the expression)

   D	M	W	Alarm
   0	0	0	0
   0	1	0	0
   1	0	0	0
   1	1	0	1
   0	0	1	1
   0	1	1	1
   1	0	1	1
   1	1	1	1

Example 2 – From a truth table (no simplification required)

Given truth table (3 inputs A, B, C)

Step 1 – Write the canonical sum‑of‑products (SOP) expression

Write a product term for each row where F = 1:

• Row 2:  ¬A · ¬B · C
• Row 3:  ¬A · B · ¬C
• Row 5:  A · ¬B · ¬C
• Row 8:  A · B · C

Thus, F = (¬A·¬B·C) + (¬A·B·¬C) + (A·¬B·¬C) + (A·B·C)

Step 2 – Convert each product term into a small sub‑circuit

• Use AND gates for the three‑input products.