teach me like i know nothing, COMPUTER SCIENCE 047... Summary & Study Notes

TERM2 REVISION WORKSHEETI.pdf 📝

• This is a revision worksheet for the course labelled "0478 ComputerScience" covering Chapter 4 and Chapter 10 with numbered questions and blank answer slots.
• The file contains placeholders for answers (ANS) but no worked solutions, so it is a prompt to practice and check answers against a textbook or teacher notes.

What this source is for

• Use it as a practice checklist of topics you must be able to answer from Chapters 4 and 10.
• Treat each numbered item as a short test: write the answer, then justify each step.

How to use this worksheet (step-by-step)

1. Read a question and identify the underlying topic in one phrase (e.g., "binary conversion", "encryption").
2. Recall or look up the atomic definition of the main terms in the question.
3. Solve by writing numbered steps or showing arithmetic—never just give a final number.
4. Cross-check your answer against the textbook (the other source in these notes) or ask your teacher.

Smallest building blocks to apply to each question

• Ask: what is the input type? (number, binary string, image specs, text)
• Ask: what is the desired output? (binary, hex, checksum, file size)
• List the formulas or methods you need (division method, positional weights, sampling rate × bits × time).

Example approach (applies to most worksheet questions)

• If question is "convert denary to binary":
  1. Identify the number and required bit-length.
  2. Use repeated division by 2 or subtract powers of two (choose one method).
  3. Write final binary with leading zeros if bit-length required.
• If question is "calculate file size":
  1. Multiply pixels × bits per pixel for images, or sample rate × bit depth × channels × seconds for audio.
  2. Convert bits to bytes and then to KB/MB using appropriate unit system.

Quick checklist to mark your answers

• Did I show each step? (Yes / No)
• Did I label units and bit-length? (Yes / No)
• Could an off-by-one or overflow error change my answer? (Check range limits)

Key terms to remember from this worksheet

• Revision worksheet — a set of practice questions for exam preparation
• Chapter 4 — (use textbook to map topics)
• Chapter 10 — (use textbook to map topics)

Suggested next action

• Take each blank (ANS) and attempt to solve using the course book section on number systems, encoding, and CPU fundamentals in the companion source.

Computer science Course book.pdf 📘

• This source is a condensed summary of the Cambridge IGCSE/O Level Computer Science Student Book and supporting materials covering data representation, algorithms, programming and computer systems.
• It explains number systems (binary/hex), encoding (text, images, sound), data storage and compression, error detection, encryption, CPU/memory architecture, and embedded systems.

Foundations: what a number system is

• A number system defines symbols and a base that sets the value of each digit position.
• For denary (decimal) the base is 10 and each position represents powers of 10; for binary the base is 2 and positions represent powers of 2.
• binary — uses digits 0 and 1; each bit is a single binary digit.

Two methods to convert denary to binary (small steps)

• Method 1: Subtract powers of two (positional method).
  1. Find the largest power of 2 ≤ the number (powers: $2^0,2^1,2^2,...$).
  2. Subtract it, put 1 in that bit position, repeat with remainder.
  3. Fill lower unused positions with 0.
• Method 2: Repeated division by 2 (remainder method).
  1. Divide the number by 2, record remainder (0 or 1).
  2. Repeat with the quotient until quotient is 0.
  3. Read remainders in reverse order to get the binary number.

Worked example: convert 59 to binary (both methods)

• Method 1 (powers):
  1. Largest power ≤ 59 is $2^5=32$; 59−32=27 → bit for $2^5$ is 1.
  2. Next $2^4=16$ ≤ 27; 27−16=11 → bit for $2^4$ is 1.
  3. $2^3=8$ ≤ 11; 11−8=3 → bit for $2^3$ is 1.
  4. $2^2=4$ > 3 → bit for $2^2$ is 0.
  5. $2^1=2$ ≤ 3; 3−2=1 → bit for $2^1$ is 1.
  6. $2^0=1$ ≤ 1; 1−1=0 → bit for $2^0$ is 1.
  7. Binary: 00111011 (showing 8 bits).
• Method 2 (division):
  1. 59 ÷ 2 = 29 rem 1
  2. 29 ÷ 2 = 14 rem 1
  3. 14 ÷ 2 = 7 rem 0
  4. 7 ÷ 2 = 3 rem 1
  5. 3 ÷ 2 = 1 rem 1
  6. 1 ÷ 2 = 0 rem 1
  7. Read remainders upward: 111011 → pad to 8 bits: 00111011

Hexadecimal basics and conversions (small pieces)

• Hex is base 16 using 0–9 then A–F where A=10 to F=15.
• Each hex digit maps exactly to 4 binary bits; group binary in fours from the right to convert easily.

Example: binary → hex

• Binary 11011111 → group: 1101 1111 → hex digits D F → result: DF.

Example: hex → denary

• Hex 1A3 means (1×16^2) + (10×16^1) + (3×16^0) = 256 + 160 + 3 = 419.

Converting denary to hex (division method)

1. Repeatedly divide by 16, recording remainders.
2. Read remainders in reverse to get hex digits.

Key term to memorize

• hexadecimal — base-16 representation useful for compact binary display.

Binary addition, overflow and carries (stepwise)

• Addition rules: 0+0=0, 0+1=1, 1+1=0 with carry 1, 1+1+1=1 with carry 1.
• If adding two n-bit numbers produces an (n+1)-th bit 1, that is an overflow for fixed n-bit storage.

Example: adding two 8-bit numbers (conceptual)

1. If sum > 255 then you will generate a ninth bit and data will not fit into 8 bits.
2. Detect overflow by checking the carry out of the most significant bit.

Logical shifts (small concept)

• Shifting left by one moves all bits one place left and fills the rightmost bit with 0; it multiplies the numeric value by 2 if no bits are lost.
• Shifting right divides by 2 (discarding remainder) and fills leftmost with 0 for logical shift.
• Shifting beyond bit-width can discard significant bits and cause errors.

Two's complement representation (stepwise)

• Purpose: represent negative integers in binary with the same addition rules.
• For n-bit two's complement:
  1. Positive numbers: standard binary representation with left-most bit 0.
  2. Negative numbers: take absolute value in binary, invert bits, add 1.
  3. Range for 8 bits: -128 to +127.

Example: convert -18 to 8-bit two's complement

1. +18 in binary: 00010010.
2. Invert bits: 11101101.
3. Add 1: 11101101 + 1 = 11101110.
4. So -18 = 11101110 (8-bit two's complement).

Character encoding: ASCII vs Unicode (concise)

• ASCII — standard 7-bit codes for basic English characters; extended ASCII uses 8 bits for extra symbols.
• Unicode — supports many languages and symbols, uses up to 4 bytes per character depending on encoding (e.g., UTF-8 variable length).

Sound representation (small bits)

• Analog sound is sampled at a regular rate; each sample records amplitude with a certain bit depth (resolution).
• File size for PCM audio = sample rate × bit depth × channels × duration (in seconds).

Audio example: compute storage quickly

• For 10 seconds, mono, 16-bit, 44,100 Hz:
  1. Samples = 44,100 × 10 = 441,000 samples.
  2. Bits = 441,000 × 16 = 7,056,000 bits.
  3. Bytes = 7,056,000 ÷ 8 = 882,000 bytes ≈ 861 KB.

Image representation and file size

• Bitmaps store every pixel's color; color depth = bits per pixel (bpp).
• File size (bits) = width × height × bpp. Convert to bytes then KB/MB.

Example: bitmap size

• 4096 × 3072 pixels at 24 bpp:
  1. Pixels = 4096 × 3072 = 12,582,912.
  2. Bits = 12,582,912 × 24 = 301,990, (approx) 301,989,888 bits.
  3. Bytes ≈ 37,748,736 bytes ≈ 36 MB.

Data units and measurements

• Bits and bytes; larger units KB, MB, GB, TB can be SI (1000-based) or binary (1024-based); memory sizes commonly use binary.

Compression: lossy vs lossless (core ideas)

• Lossless compression: original data can be perfectly reconstructed (example: Run-Length Encoding, RLE).
• Lossy compression: reduces file size by discarding some data that is less noticeable (examples: JPEG for images, MP3 for audio).
• lossless compression — use when exact data is required (e.g., text, some images).

RLE (Run-Length Encoding) example and steps

1. Replace runs of the same value with a count and the value.
2. Example: AAAA B B B C C → 4A 3B 2C.
3. Works best with lots of repetition; useless on already random data.

Data transmission and bandwidth

• bandwidth — maximum data transfer rate over a network link, measured in kbps or Mbps.
• Higher bandwidth allows faster transfer of large files but is affected by latency and congestion.

Error detection methods (small pieces)

• Parity check: add a single parity bit to make the number of 1-bits even (even parity) or odd (odd parity); detects single-bit errors.
• Checksums: compute a numeric summary of a block and send it with data; receiver recalculates and compares.
• Echo checks: receiver returns data to sender for comparison; simple but slow.
• Check digits: extra digit calculated from others to detect entry errors (used in barcodes/ISBN).
• ARQ (Automatic Repeat reQuest): receiver sends ACK/NACK; on error sender retransmits.

Example: parity check quick idea

• Byte 1011001 has four 1s; even parity bit would be 0 (keeps total 4 even); if receiver sees odd count it flags error.

Encryption basics (small steps)

• Symmetric encryption: same secret key used for encryption and decryption; fast but key distribution is a challenge.
• asymmetric encryption: uses a public key for encryption and a private key for decryption; keys come in pairs.

Tom & Jane example (step-by-step)

1. Jane generates a key pair: public key (shareable) and private key (keep secret).
2. Jane sends public key to Tom.
3. Tom encrypts the document using Jane's public key and sends ciphertext.
4. Jane decrypts using her private key and reads the document.

Error detection vs encryption note

• Error detection ensures data integrity; encryption ensures confidentiality. Both can be used together.

CPU and memory basics (small building blocks)

• MDR (Memory Data Register) — temporarily holds data moving to/from memory.
• MAR (Memory Address Register) — holds the address for the memory operation.
• PC (Program Counter) — holds address of next instruction to fetch.
• System buses:
  • Address bus: unidirectional, carries addresses.
  • Data bus: bidirectional, carries actual data.
  • Control bus: carries control signals (read/write, interrupts).

Fetch–Decode–Execute cycle (numbered steps)

1. Fetch: CPU places address from PC into MAR, sends read signal, data returned into MDR.
2. Decode: instruction in MDR is decoded by control unit to determine actions.
3. Execute: ALU or control signals perform the operation; PC is updated to next instruction.

Factors affecting CPU performance (small list)

• Clock speed (higher → more instructions per second).
• Bus width (wider → more bits transferred at once).
• Cache memory (faster access reduces wait time).
• Number of cores (more cores → parallel tasks but need parallelisable work).

Embedded systems (stepwise idea)

• Definition: a dedicated combination of hardware and software designed to perform a specific task.
• Examples: microcontrollers in washing machines, voting machines, vehicle control units, smart thermostats.
• Trade-offs: efficient and small but can be hard to upgrade or debug.

Practice problems and worked solutions (from the course book examples)

Problem: Convert 59 (denary) to binary

Solution:

1. Use division method: 59 ÷ 2 = 29 rem 1; 29 ÷ 2 = 14 rem 1; 14 ÷ 2 = 7 rem 0; 7 ÷ 2 = 3 rem 1; 3 ÷ 2 = 1 rem 1; 1 ÷ 2 = 0 rem 1.
2. Read remainders upward: 111011; pad to 8 bits: 00111011.
3. Answer: 00111011.

Problem: Convert binary 11011111 to hex

Solution:

1. Group bits into fours from right: 1101 1111.
2. Convert groups to hex: 1101 = D, 1111 = F.
3. Answer: DF.

Problem: Add two 8-bit numbers and show overflow (example)

Given: 11011111 (223) + 10000010 (130). Solution:

1. Add decimal values: 223 + 130 = 353.
2. 8-bit max unsigned value = 255; 353 > 255 so result needs 9 bits.
3. Overflow occurs because the ninth bit would be 1; in 8-bit storage this overflows and low 8 bits only represent 353 − 256 = 97.
4. Answer: Overflow detected; stored 8-bit result equals binary of 97 if truncated.

Problem: Compress AAAAABBBBCC using RLE

Solution:

1. Count runs: 5 A, 4 B, 2 C.
2. RLE result: 5A 4B 2C.
3. Answer: 5A4B2C.

Final key terms to review from this source

• two's complement, binary, hexadecimal, asymmetric encryption.

Suggested study path using this source

1. Master conversions (denary↔binary↔hex) with both methods and many examples.
2. Practice binary arithmetic and detect overflow cases.
3. Solve file-size and sampling problems until fast and accurate.
4. Learn error-detection methods and run small examples by hand.
5. Understand CPU registers and execute the fetch-decode-execute cycle on paper for short programs.