Dual-Board Mastery: Cambridge IGCSE 0417 & WASSCE Digital Technology
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WEEK 01 CURRICULAR SUITE
Systems Architecture, Number Bases & Data Representation
Syllabus Alignment: Cambridge 0417 Units 1 & 3; WASSCE Computer Studies (Positional Number Systems) Mission Objective: Master positional number systems (Base 2, 8, 10, 16), binary arithmetic, and internal CPU architecture to solve external theory and calculation questions with 100% accuracy.
• Hexadecimal Advantage: 1 hex digit represents exactly 4 binary bits (1 nibble). Example: 1111 1010₂ = FA₁₆. It reduces long binary strings, minimizing human transcription errors in memory dumps and MAC/IPv6 addresses.
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• Octal & Number Base Conversions: Octal (Base 8) groups binary bits into sets of 3 (since 2³ = 8). Hexadecimal (Base 16) groups bits into sets of 4 (since 2⁴ = 16). Positional values in octal are 8⁰=1, 8¹=8, 8²=64, 8³=512.
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• CPU Architecture: Central Processing Unit contains the Arithmetic Logic Unit (ALU for calculations and boolean logic), Control Unit (CU for managing the fetch-decode-execute cycle), and high-speed registers (PC, MAR, MDR, Accumulator).
★ Cambridge / WAEC Model Scenario:
Convert decimal number 142 into (a) 8-bit Binary, and (b) Hexadecimal.
💡 Worked Solution & Rationale:
Step 1: Convert to Binary by successive division by 2 or positional weights (128, 64, 32, 16, 8, 4, 2, 1): 142 = 128 + 0 + 0 + 14 = 128 + 0 + 0 + 8 + 4 + 2 + 0 -> Binary: 10001110₂. Step 2: Convert to Hexadecimal by splitting the 8-bit binary into two 4-bit nibbles: Left nibble: 1000₂ = 8 | Right nibble: 1110₂ = 8 + 4 + 2 = 14 = E₁₆. Final Hexadecimal = 8E₁₆.
🃏 Key Words — Click a Card to Reveal the Definition
6 Terms
Card 01
Binary (Base 2)
👆 Click / Tap to Reveal Definition
Definition 01
Positional numbering system using only digits 0 and 1, matching the on/off states of computer transistors.
Card 02
Hexadecimal (Base 16)
👆 Click / Tap to Reveal Definition
Definition 02
Compact numbering system (0-9, A-F) where 1 hex digit represents exactly 4 binary bits (one nibble).
Card 03
Octal (Base 8)
👆 Click / Tap to Reveal Definition
Definition 03
Positional numbering system using digits 0 to 7, where each octal digit corresponds to exactly 3 binary bits (2³ = 8).
Card 04
ALU (Arithmetic Logic Unit)
👆 Click / Tap to Reveal Definition
Definition 04
CPU component responsible for performing arithmetic operations (+, -, *, /) and Boolean logical decisions.
Card 05
Control Unit (CU)
👆 Click / Tap to Reveal Definition
Definition 05
Directs the flow of instructions and data through the CPU during the Fetch-Decode-Execute cycle.
Card 06
Registers
👆 Click / Tap to Reveal Definition
Definition 06
High-speed internal memory storage locations inside the CPU (e.g. PC, MAR, MDR, Accumulator).
🕵️ Common Exam Mistakes — Can You Spot the Error?
Examiner Trap
⚠️ Candidate Error Trap:
A student wrote in an exam: 'The number 78A is a valid Octal number because it starts with 7.'
🎯 Your Detective Mission:
Identify the two fatal errors in the student's statement and explain the rule of positional number bases.
✅ Official Examiner Solution:
Error 1: The octal number system (Base 8) only uses digits 0 through 7. The symbol '8' does not exist in octal. Error 2: The symbol 'A' represents 10 in hexadecimal (Base 16) and is invalid in octal. Correction: The number 78A is a Hexadecimal number, not an Octal number.
📝 Quiz — Test Yourself (10 Questions)
Instant Marking & Explanation
1. Which digits are valid in the octal number system?
A) 0 to 8
B) 0 to 7
C) 1 to 8
D) 0 and 1
Mark Scheme Rationale: Octal (Base 8) uses only symbols 0 through 7.
2. What is the decimal equivalent of the binary number 1011₂?
A) 9
B) 10
C) 11
D) 13
Mark Scheme Rationale: 8 + 0 + 2 + 1 = 11.
3. What is the hexadecimal equivalent of decimal 15?
A) E
B) F
C) 10
D) 15
Mark Scheme Rationale: 15 in hexadecimal is represented by the single symbol F.
4. How many binary bits are represented by a single hexadecimal digit?
A) 2 bits
B) 4 bits
C) 8 bits
D) 16 bits
Mark Scheme Rationale: Each hexadecimal digit corresponds to exactly 4 bits (1 nibble).
5. Which of the following numbers cannot be a binary number?
A) 1001
B) 1101
C) 1021
D) 1111
Mark Scheme Rationale: Binary uses only digits 0 and 1. The digit '2' is invalid.
6. What is the hexadecimal representation of the binary byte 1101 1011₂?
A) DB₁₆
B) BD₁₆
C) 13B₁₆
D) D11₁₆
Mark Scheme Rationale: 1101₂ = 13 = D; 1011₂ = 11 = B. Result: DB₁₆.
7. What is the result of binary addition: 1010₂ + 0101₂?