Overview
Data representation defines how information is stored, structured, and interpreted in a computer system using binary values. It forms the foundation for how data is processed at the hardware level.
Terminology
| Term | Definition |
|---|---|
| Bit | 1 binary digit |
| Nibble | 4 bits (e.g., 1101) |
| Byte | 8 bits (e.g., 1101 1110) |
| Word | 16 bits (2 bytes) |
| Double Word | 32 bits (4 bytes) |
| Quad Word | 64 bits (8 bytes) |
| Positional Notation | System for representing numbers based on position (e.g., binary) |
| Base | The number of unique digits used in a number system (e.g., base 10) |
| Most Significant Bit (MSB) | Leftmost bit; also represents the sign in signed integers |
| Least Significant Bit (LSB) | Rightmost bit |
Core Concepts
Number Systems
Data sizes typically scale in powers of 2. Computers use multiple number systems to represent values efficiently.
| System | Base | Digits Used |
|---|---|---|
| Binary | Base 2 | 0, 1 |
| Octal | Base 8 | 0–7 |
| Decimal / Denary | Base 10 | 0–9 |
| Hexadecimal | Base 16 | 0–9, A–F |
Signed Integers
- The Most Significant Bit (MSB) represents the sign:
0→ Positive1→ Negative
- One bit is reserved for the sign; remaining bits represent the magnitude
Floating Point Representation
Used to represent real numbers (numbers with decimals). Based on the IEEE 754 standard.
| Component | Role |
|---|---|
| Sign Bit | Indicates positive or negative |
| Exponent | Determines scale |
| Mantissa (Significand) | Stores the precision value |
- Common formats: 32-bit (single precision), 64-bit (double precision)
- Enables efficient representation of very large and very small numbers
Related Concepts
Related Techniques
Related Tools
References / Images
- Binary/hex conversion charts
- IEEE 754 diagrams