Four binary bits correspond exactly to one hex digit because 2⁴ = 16.
Binary → Hex: Split the binary number into groups of four starting at the right‑most bit, add leading zeros if needed, then replace each group with its hex equivalent.
Hex → Binary: Replace each hex digit with its 4‑bit binary equivalent.
Example: 1101 0110₂ → groups 1101 0110 → D 6 → D616.
In an n‑bit unsigned word the largest value is 2ⁿ‑1. Adding two numbers whose sum exceeds this limit discards the high‑order carry – the stored result is wrong (overflow).
Example (8‑bit unsigned):
Operand A
Operand B
Exact 9‑bit sum
Stored 8‑bit result
200₁₀ = 11001000₂
100₁₀ = 01100100₂
11001100₂ (carry 1)
1001100₂ = 44₁₀ (overflow)
Two’s‑Complement (signed integers)
Write the absolute value in binary using the required number of bits.
Invert every bit (0→1, 1→0).
Add 1 to the inverted pattern.
Example: Represent ‑25 in an 8‑bit word.
25₁₀ = 00011001₂
Invert → 11100110₂
Add 1 → 11100111₂ → stored pattern for ‑25₁₀
To convert a two’s‑complement word back to decimal:
If the left‑most bit is 0, treat it as ordinary binary.
If the left‑most bit is 1, invert, add 1, then prefix a minus sign.
Logical Shifts
Logical left shift (<<): bits move left, 0 inserted on the right. Equivalent to multiplying by 2 (ignoring overflow).
Logical right shift (>>): bits move right, 0 inserted on the left. Equivalent to integer division by 2 (floor).
Example (8‑bit): 00110101₂ << 1 → 01101010₂ (53₁₀ → 106₁₀).
2. Computer Systems – Hardware
2.1 Central Processing Unit (CPU)
Fetch‑Decode‑Execute cycle – the CPU repeatedly fetches an instruction from memory, decodes it, and executes it.
Clock speed – measured in MHz or GHz; determines how many cycles occur per second.
Registers – small, fast storage inside the CPU (e.g., accumulator, program counter).
ALU (Arithmetic‑Logic Unit) – performs arithmetic and logical operations.
Cache – a small, fast memory that stores frequently used data/instructions.
Multi‑core processors – more than one execution unit on a single chip, allowing parallel processing.
Definition: a step‑by‑step procedure for solving a problem.
Characteristics: finite, unambiguous, effective.
Common structures: sequence, selection (if‑else), iteration (loops).
Complexity: time (how many steps) and space (memory used).
6.2 Pseudocode Conventions (Cambridge style)
DECLARE counter, total AS INTEGER
SET counter ← 1
SET total ← 0
WHILE counter ≤ 10 DO
SET total ← total + counter
SET counter ← counter + 1
END WHILE
OUTPUT total
6.3 Flowchart Symbols
Symbol
Name
Purpose
▭
Process
Assignment, calculation
◇
Decision
True/False test (if‑else)
▶︎
Input/Output
Read or display data
○
Connector
Linking flow lines
⬚
Start/Stop
Begin or end of algorithm
6.4 Programming Concepts (Python‑style examples)
Variables & Data Types
age = 15 # integer
price = 3.99 # float
name = "Alice" # string
is_valid = True # boolean
Control Structures
# Selection
if score >= 50:
result = "Pass"
else:
result = "Fail"
# Iteration (for loop)
total = 0
for i in range(1, 11): # 1 to 10 inclusive
total = total + i
Functions (modular programming)
def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
6.5 Problem Solving Strategies
Understand the problem – read the question carefully.
Identify inputs, required outputs and constraints.
Design an algorithm – use pseudocode or a flowchart.
Implement the algorithm in a programming language.
Test with a range of data, including edge cases.
Analyse efficiency (big‑O notation) if required.
7. Logic & Boolean Algebra
7.1 Logic Gates
Gate
Symbol
Truth Table
AND
∧
1 & 1 → 1; otherwise 0
OR
∨
0 ∨ 0 → 0; otherwise 1
NOT
¬
¬0 → 1, ¬1 → 0
NAND
↑
inverse of AND
NOR
↓
inverse of OR
XOR
⊕
1 ⊕ 0 → 1; 0 ⊕ 1 → 1; otherwise 0
7.2 Boolean Expressions & Simplification
Use identities: A ∧ (A ∨ B) = A, A ∨ (A ∧ B) = A, ¬(A ∧ B) = ¬A ∨ ¬B (De Morgan).
Convert truth tables to expressions (sum‑of‑products) and simplify.
7.3 Logic Circuits – Example
Design a circuit that outputs 1 when exactly two of three switches (A, B, C) are ON.
Expression: (A ∧ B ∧ ¬C) ∨ (A ∧ ¬B ∧ C) ∨ (¬A ∧ B ∧ C)
Implement with AND, OR, NOT gates as shown in the accompanying diagram (exam‑style).
8. Revision Checklist
Convert between denary, binary and hexadecimal (both directions) – be able to do it by hand.
Explain overflow and two’s‑complement with examples.
Describe the CPU cycle, registers, cache and main memory.
Identify input/output device categories and give real‑world examples.
Calculate file sizes for audio, images and text using the appropriate formulas.
Write clear pseudocode/flowcharts for simple algorithms (e.g., sum of numbers, factorial).
Construct and simplify Boolean expressions; recognise basic logic gates.
Understand basic networking concepts: IP, DNS, TCP/UDP, bandwidth vs latency.
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