Describe the principal methods of representing data

• Computers store all data in binary using 0 and 1.
• Different data types use different encodings.

Integers

• Whole numbers use binary place value.
• Each bit position = a power of 2.
• Example: 10110101₂ = 181₁₀

Negative integers

• Usually use two’s complement — efficiently stores positive and negative values.
• In an 8-bit system:
  • 00000101 = +5
  • 11111011 = -5

Real numbers

Numbers with fractional parts can use:

• Fixed-point representation
  • Fixed bits for integer and fractional parts.
  • Simple but limited range/precision.
• Floating-point representation
  • Stores a number using sign, exponent, and mantissa/significand.
  • Allows a very wide range.
  • May introduce rounding errors.

Text

Each character is stored using a binary code. Common systems:

• ASCII
  • Originally 7 bits.
  • Suitable for English letters, digits, symbols.
• Unicode
  • Supports a much larger character set across languages.
  • Commonly implemented using UTF-8 or UTF-16.

Images

• Images represented as pixels; each pixel stores a colour value.
• Storage depends on:
  • Resolution — number of pixels.
  • Colour depth — bits per pixel.
• Examples:
  • 1-bit: each pixel is black or white.
  • 8-bit: 256 possible values.
  • 24-bit: 8 bits each for red, green, blue.

Sound

• Sound represented by sampling an analogue wave at regular intervals.
• Each sample is quantized and stored in binary.
• Quality depends on:
  • Sampling rate — samples per second.
  • Bit depth — bits per sample.

Boolean data

• Stores only two possible states:
  • true / false
  • 1 / 0
  • on / off
• Heavily used in logic circuits and programming conditions.