Chapter 1 – Information Representation

1.1 Data Representation  

Key Terms  

- Binary → Base‑2 system (0,1).  

- Bit → Binary digit.  

- One’s Complement → Invert each digit.  

- Two’s Complement → Invert digits + add 1 (negative numbers).  

- Sign & Magnitude → Left‑most bit = sign (0 positive, 1 negative).  

- Hexadecimal → Base‑16 (0–9, A–F).  

- Memory Dump → Printout of memory contents.  

- BCD (Binary‑Coded Decimal) → 4 bits per decimal digit.  

- ASCII → 7‑bit character encoding.  

- Unicode → Universal encoding for all languages.  

1.1.1 Number Systems  

- Denary (Decimal) → Base 10.  

- Binary → Base 2.  

- Hexadecimal → Base 16.  

Conversions  

- Binary → Denary: Add place values of 1s.  

- Denary → Binary: Successive division by 2.  

- Binary Addition: Carry when sum > 1.  

- Binary Subtraction: Use two’s complement.  

1.1.2 Binary Number System  

- Binary addition example:  

  - 0101 + 0011 = 1000.  

- Overflow → Result exceeds available bits.  

1.1.3 Hexadecimal Number System  

- Hex → Binary: Each hex digit = 4 bits.  

- Binary → Hex: Group in 4s.  

- Example: Hex A3 = Binary 10100011.  

- Use → Memory dumps (compact, readable).  

1.1.4 Binary‑Coded Decimal (BCD)  

- 4 bits per decimal digit.  

- Example: 45 = 0100 0101.  

- Used in calculators and clocks.  

1.1.5 ASCII & Unicode  

- ASCII → 7‑bit (extended 8‑bit).  

- Unicode → Global standard, first 128 = ASCII.  

- Example: ‘A’ = Binary 01000001 (Hex 41).  

1.2 Multimedia  

1.2.1 Bit‑Map Images  

- Pixels in a grid.  

- Resolution → number of pixels.  

- Colour Depth → bits per pixel.  

- File size = Resolution × Color Depth.  

- Example: 1920×1080, 24‑bit → 49,766,400 bits.  

1.2.2 Vector Graphics  

- Defined by equations, not pixels.  

- Scalable without quality loss.  

- Formats: .svg, .cgm, .odg.  

- Smaller file size, less realistic.  

1.2.3 Sound Files  

- Analog → digitized.  

- Sampling → measure amplitude at intervals.  

- Resolution → bits per sample.  

- Rate → samples per second.  

- Example: CD = 16‑bit, 44.1 kHz.  

1.2.4 Video  

- Sequence of frames.  

- Frame Rate → 24, 30, 60 fps.  

1.3 File Compression  

Key Terms  

- Lossless → No data lost (ZIP, PNG, GIF).  

- Lossy → Some data discarded (JPEG, MP3, MP4).  

- RLE (Run‑Length Encoding) → Replace repeated values with count.  

1.3.1 Lossless vs Lossy  

- Lossless → Perfect recovery, larger files. Best for text/software.  

- Lossy → Smaller files, quality loss. Best for multimedia.  

1.3.2 Applications  

- MP3 → Audio compression (~90% smaller).  

- MP4 → Multimedia (video, audio, text).  

- JPEG → Images, discards subtle differences.  

- RLE → Effective for repetitive data (e.g., “AAAAABBBCCCC” → “5A3B4C”).  

Summary:  

- Binary, Hex, ASCII, Unicode → core of data representation.  

- Multimedia → stored via bitmaps, vectors, sound sampling, video frames.  

- Compression → Lossless for accuracy, Lossy for efficiency.