Use logic gates to create logic circuits from a problem statement, logic expression or truth table

Cambridge IGCSE Computer Science (0478) – Complete Revision Notes

How the marks are allocated

Assessment Objective	What it tests	Typical weighting
AO1 – Knowledge & understanding	Recall of facts, definitions, terminology and basic concepts.	≈ 30 %
AO2 – Application	Use knowledge to interpret questions, construct tables, write short programmes, draw circuits, etc.	≈ 35 %
AO3 – Analysis & evaluation	Explain reasoning, justify choices, compare alternatives, optimise solutions.	≈ 35 %

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1 Computer Systems

1.1 Data representation

• Binary (base‑2) – each digit is a bit. 8 bits = 1 byte.
• Denary (base‑10) ↔ Binary
  • Division‑by‑2 method for conversion to binary.
  • Multiplication‑by‑2 method for conversion to denary.
  • Example: 156₁₀ → 10011100₂.
• Hexadecimal (base‑16) – digits 0‑9 and A‑F.
  • Binary ↔ Hex: group binary in sets of four.
  • Example: 1010 1101₂ → AD₁₆.
• Binary addition – include overflow flag (carry out of the most‑significant bit).
• Text – ASCII (7‑bit) or Unicode (up to 21 bits). Example: ‘A’ = 65₁₀ = 01000001₂.
• Images – bitmap (pixel colour depth) vs vector.
• Sound – sampled at 44 kHz, 16‑bit gives 2⁴⁴ ≈ 7 × 10⁹ possible values per second.

1.2 Transmission of data

• Analogue vs digital signals.
• Bandwidth, latency, error‑checking (parity, checksum, CRC).
• Common media: twisted‑pair, coaxial, fibre‑optic, wireless (Wi‑Fi, Bluetooth).

1.3 Hardware components

• CPU – control unit, ALU, registers, cache.
• Memory hierarchy – primary (RAM), secondary (HDD/SSD), tertiary (magnetic tape, cloud).
• Input devices (keyboard, mouse, scanner) and output devices (monitor, printer, speaker).
• Motherboard, bus, power supply, ports.

1.4 Software

• System software – operating system, device drivers, utility programmes.
• Application software – word processors, spreadsheets, databases, web browsers.
• Freeware, shareware, open‑source, proprietary licences.

1.5 The internet & its protocols

• Client‑server model, IP addressing (IPv4 4 × 8‑bit octets), DNS.
• Common protocols: HTTP/HTTPS, FTP, SMTP, POP3/IMAP.
• Security basics – firewalls, encryption (AES, RSA), authentication.

1.6 Emerging technologies

• Internet of Things (IoT), cloud computing, artificial intelligence, robotics, 3‑D printing.
• Potential impact on society, ethical considerations, sustainability.

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2 Algorithms & Problem Solving (Topic 7)

2.1 The programme development life‑cycle

1. Analyse the problem.
2. Design an algorithm (flowchart or pseudocode).
3. Write the programme.
4. Test & debug.
5. Document and maintain.

2.2 Flowchart symbols (Cambridge standard)

Symbol	Name	Purpose
▭	Process	Assignment, calculation, I/O.
◇	Decision	True/false test.
▶︎	Start/Stop	Entry and exit points.
⇆	Input/Output	Read or display data.
↺	Loop	Repeated execution (while/for).

2.3 Pseudocode conventions (required by the exam)

• Variables are written in lower‑case letters.
• Assignment: var ← expression
• Input: READ var Output: WRITE expression
• Decision: IF condition THEN … ENDIF
• Loop: WHILE condition DO … ENDWHILE or FOR i ← 1 TO n DO … ENDFOR

2.4 Trace tables

Show the values of all variables after each step of an algorithm. Essential for AO2 marks.

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3 Programming Concepts (Topic 8)

3.1 Variables, data types & operators

• Primitive types: INTEGER, REAL, BOOLEAN, CHARACTER, STRING.
• Operators: arithmetic (+, –, *, /, %), relational (=, ≠, <, >, ≤, ≥), logical (AND, OR, NOT).

3.2 Control structures

• Sequence – statements executed in order.
• Selection – IF…THEN…ELSE, CASE.
• Repetition – WHILE, FOR, REPEAT…UNTIL.

3.3 Arrays (single‑dimensional)

• Declaration: DIM A(10) AS INTEGER (indices 0‑9 or 1‑10 depending on language).
• Access: A[i].
• Common operations – initialise, traverse, search, sort (bubble, insertion).

3.4 File handling (basic)

• Open a file (OPEN), read/write (READ, WRITE), close (CLOSE).
• Sequential access only – required for the exam.

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4 Databases & SQL (Topic 9)

4.1 Database design basics

• Single‑table database – primary key uniquely identifies each record.
• Choose appropriate data types (INTEGER, REAL, CHAR, VARCHAR, DATE).
• Normalisation is not required for IGCSE, but avoid duplicate columns.

4.2 The five SQL commands examined

Command	Purpose	Typical syntax
SELECT	Retrieve data	SELECT column1, column2 FROM table WHERE condition;
INSERT	Add a new record	INSERT INTO table (col1, col2) VALUES (val1, val2);
UPDATE	Modify existing records	UPDATE table SET col1 = val1 WHERE condition;
DELETE	Remove records	DELETE FROM table WHERE condition;
CREATE TABLE	Define a new table	CREATE TABLE table (col1 TYPE, col2 TYPE, …);

4.3 Query‑building tips for the exam

• Always write column names in the same order as they appear in the table unless SELECT * is used.
• Remember that WHERE conditions use the same relational operators as in pseudocode.
• Test your query mentally with a small data set to avoid logical errors.

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5 Boolean Logic – Logic Gates (Topic 10)

5.1 Learning objective

Use logic gates to create logic circuits from a problem statement, a Boolean expression, or a truth table.

5.2 Key concepts

• Boolean variables: 0 = FALSE, 1 = TRUE.
• Primary operators (exam‑required): AND (·), OR (+), NOT (‾).
  Other gates (XOR, NAND, NOR, XNOR) may appear, but you must be able to rewrite them using only AND, OR, NOT.
• Truth tables – list the output for every possible combination of inputs.
• Logic expressions – algebraic form of the required condition.
• Simplification – Boolean algebra or Karnaugh maps to minimise the number of gates.
• Implementation – converting an expression or truth table into a circuit diagram.

5.3 Standard Cambridge gate symbols

Gate	Symbol	Boolean function
AND		A·B
OR		A+B
NOT		‾A
NAND		‾(A·B)
NOR		‾(A+B)
XOR		A⊕B
XNOR		‾(A⊕B)

Truth‑table definitions for each gate

Gate	Inputs	Output
AND	A B	1 only for 1 1
OR	A B	0 only for 0 0
NOT	A	1 when A = 0, 0 when A = 1
NAND	A B	0 only for 1 1
NOR	A B	1 only for 0 0
XOR	A B	1 for 0 1 and 1 0
XNOR	A B	1 for 0 0 and 1 1

5.4 General design process

1. Interpret the problem. List every input variable and the exact condition that makes the output true.
2. Write a Boolean expression. Use AND, OR, NOT (or other gates if given) to model the condition.
3. Construct a truth table. Include all 2ⁿ rows for n inputs.
4. Simplify (optional but valuable). Apply Boolean algebra or a Karnaugh map to reduce gate count.
5. Draw the circuit. Replace each operator in the (simplified) expression with its gate symbol; use only AND, OR, NOT unless you explicitly show the equivalent network.

5.5 Checklist – Common pitfalls

• ✔️ All possible input combinations must appear in the truth table.
• ✔️ When an XOR, NAND, NOR, or XNOR is given, write the equivalent expression using only AND, OR, NOT before drawing the final circuit.
• ✔️ Verify the truth table after every simplification step – a single wrong minterm loses marks.
• ✔️ Keep the gate count low; a simpler circuit demonstrates AO3 analysis.
• ✔️ Label inputs and outputs clearly on the diagram.

5.6 Full worked example – Security system

Problem statement

Three sensors A, B and C. The alarm L sounds if sensor A is triggered **and** exactly one of sensors B or C is triggered.

Step 1 – Identify variables

• A – sensor A (1 = triggered)
• B – sensor B
• C – sensor C
• L – alarm output

Step 2 – Write the Boolean expression

“Exactly one of B or C” is an exclusive‑OR:  \(B⊕C\). Thus

\[ L = A \cdot (B⊕C) \]

If the exam only allows AND, OR, NOT, expand the XOR:

\[ B⊕C = (B + C)\;\cdot\;\overline{(B·C)} \] \[ \therefore\; L = A \cdot \big[(B + C) \cdot \overline{(B·C)}\big] \]

Step 3 – Truth table

A	B	C	B⊕C	L = A·(B⊕C)
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	0
1	0	0	0	0
1	0	1	1	1
1	1	0	1	1
1	1	1	0	0

Step 4 – Simplify (optional)

The expanded form can be rewritten as

\[ L = A\,(B+C)\,(\overline{B}+\overline{C}) \]

which is already the minimal expression for the required function.

Step 5 – Circuit diagram

• Stage 1: an XOR gate (or the equivalent OR‑AND‑NOT network) receives B and C.
• Stage 2: an AND gate receives A and the XOR output.
• The output of the AND gate is L.

5.7 Practice problem – From a truth table

Given truth table (inputs X, Y, Z; output F):

X	Y	Z	F
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	0

1. Write the minimal Boolean expression using only AND, OR, NOT (show the steps – sum‑of‑products → Karnaugh map).
2. Draw the corresponding logic‑gate circuit.

Solution outline (teacher use):

• Minterms where F = 1: m₁ (001), m₂ (010), m₄ (100).
• K‑map grouping yields \(\overline{X}Y + \overline{Y}Z + X\overline{Z}\).
• Circuit: three 2‑input AND gates (each with one NOTed input), one 3‑input OR gate.

5.8 Further practice questions

1. Write a Boolean expression that outputs 1 only when **exactly two** of the three inputs X, Y, Z are 1. Draw the minimal circuit.
2. Given the expression \(F = \overline{(P + Q)} \cdot R\), construct the truth table and sketch the circuit using only AND, OR, NOT gates.
3. Use a Karnaugh map to simplify \(H = \overline{M}N + MN + \overline{M}\overline{N}\) and then draw the simplest possible circuit.

5.9 Summary – How to earn marks for Boolean logic

• AO1 – State the correct gate symbols and write a clear Boolean expression.
• AO2 – Produce a complete truth table that matches the problem statement.
• AO3 – Simplify the expression (fewer gates = higher marks) and justify each step.
• Translate the final expression into a neat, labelled circuit diagram using the Cambridge symbols.

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6 Quick‑Reference Tables

6.1 Binary‑denary‑hex conversion cheat‑sheet

Denary	Binary (8‑bit)	Hex
0	00000000	00
10	00001010	0A
15	00001111	0F
255	11111111	FF
170	10101010	AA
85	01010101	55

6.2 Boolean algebra identities (exam‑useful)

• Identity: \(A+0=A,\;A·1=A\)
• Null law: \(A+1=1,\;A·0=0\)
• Idempotent: \(A+A=A,\;A·A=A\)
• Complement: \(A+‾A=1,\;A·‾A=0\)
• Distributive: \(A·(B+C)=A·B+A·C\)
• De Morgan: \(‾(A·B)=‾A+‾B,\;‾(A+B)=‾A·‾B\)

6.3 Common pseudocode patterns

Task	Pseudocode
Maximum of three numbers	READ a, b, c IF a > b AND a > c THEN max ← a ELSE IF b > c THEN max ← b ELSE max ← c WRITE max
Count how many of X, Y, Z are true	count ← 0 IF X = 1 THEN count ← count + 1 IF Y = 1 THEN count ← count + 1 IF Z = 1 THEN count ← count + 1 WRITE count

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7 Final Tips for Exam Day

• Read the question **twice** – underline the exact condition to be modelled.
• Start with a clear list of variables; use the same letters throughout.
• When a truth table is given, double‑check the number of rows (2ⁿ).
• For Boolean simplification, work on paper first; a clean K‑map gains marks for method.
• Label every gate, input and output in your circuit diagram – missing labels cost marks.
• Allocate time: 5 min for interpretation, 8 min for expression & truth table, 5 min for simplification, 7 min for drawing the circuit.