knowledge

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

TermDefinition
Bit1 binary digit
Nibble4 bits (e.g., 1101)
Byte8 bits (e.g., 1101 1110)
Word16 bits (2 bytes)
Double Word32 bits (4 bytes)
Quad Word64 bits (8 bytes)
Positional NotationSystem for representing numbers based on position (e.g., binary)
BaseThe 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.

SystemBaseDigits Used
BinaryBase 20, 1
OctalBase 80–7
Decimal / DenaryBase 100–9
HexadecimalBase 160–9, A–F

Signed Integers

  • The Most Significant Bit (MSB) represents the sign:
    • 0 → Positive
    • 1 → 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.

ComponentRole
Sign BitIndicates positive or negative
ExponentDetermines 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


References / Images

  • Binary/hex conversion charts
  • IEEE 754 diagrams