Number Systems and Data Representation
Computers store and process data in binary form (0s and 1s). Understanding number systems and how data is represented is fundamental for BCA students, especially for programming and computer architecture.
1. Number Systems
A number system is a way to represent numbers using digits. There are four main types used in computing:
a) Binary (Base 2)
- Uses only 0 and 1
- Each digit is called a bit
- Used internally by computers
Example:
- Decimal 5 → Binary 101
b) Octal (Base 8)
- Uses digits 0 to 7
- Often used as a shorthand for binary
Example:
- Binary 101101 → Octal 55
c) Decimal (Base 10)
- Most common system used by humans
- Uses digits 0 to 9
Example:
- Decimal 25 → Binary 11001
d) Hexadecimal (Base 16)
- Uses digits 0–9 and letters A–F
- Used in programming and memory addressing
Example:
- Binary 1111 → Hexadecimal F
2. Data Representation in Computers
Computers represent different types of data using binary:
a) Integer Representation
- Positive and negative numbers represented using signed binary (e.g., Two’s Complement)
b) Floating-Point Representation
- Used for real numbers with decimals
- Follows IEEE standards for precision and range
c) Character Representation
- Uses codes like ASCII and Unicode
- Each character is assigned a unique binary number
Example:
- ASCII code of ‘A’ → 65 → Binary 01000001
d) Boolean Representation
- Used for logical values True (1) and False (0)
Importance for BCA Students
- Essential for understanding computer programming
- Helps in designing efficient algorithms
- Important for computer architecture and networking
Example:
- Converting IP addresses from decimal to binary
- Representing colors in hexadecimal for web design
Conclusion
Number systems and data representation form the foundation of computing. Understanding binary, octal, decimal, hexadecimal, and data encoding helps BCA students work with software, hardware, and networks efficiently.