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C Programming Notes

Number Systems

Number Systems in C Programming

1. Decimal (Base-10)

This is the number system we use in everyday life
Uses digits 0-9
Example: 125 = 1×10² + 2×10¹ + 5×10⁰
In C, decimal numbers are written as is: int num = 125;

2. Octal (Base-8)

Uses digits 0-7
In C, octal numbers start with '0'
Example: 0125 (octal) = 1×8² + 2×8¹ + 5×8⁰ = 85 (decimal)
Common use cases: file permissions in Unix/Linux

3. Hexadecimal (Base-16)

Uses digits 0-9 and letters A-F (or a-f)
A=10, B=11, C=12, D=13, E=14, F=15
In C, hexadecimal numbers start with '0x' or '0X'
Example: 0x7B = 7×16¹ + 11×16⁰ = 123 (decimal)
Common use cases:
Memory addresses
Color codes (e.g., #FF0000 for red)
Binary data representation

4. Binary (Base-2)

Uses only 0 and 1
In C, binary literals start with '0b' (in C23 standard)
Example: 0b1111 = 1×2³ + 1×2² + 1×2¹ + 1×2⁰ = 15 (decimal)

Number System Conversion in C

Printf Format Specifiers

int num = 125;
printf("%d",  num);    // Decimal: 125
printf("%o",  num);    // Octal: 175
printf("%x",  num);    // Hexadecimal: 7d
printf("%X",  num);    // Hexadecimal: 7D

Reading Different Number Systems

int a, b, c;
scanf("%d", &a);  // Read decimal
scanf("%o", &b);  // Read octal
scanf("%x", &c);  // Read hexadecimal

Tips and Tricks

To identify number systems in code:
No prefix = Decimal
'0' prefix = Octal
'0x' or '0X' prefix = Hexadecimal
'0b' prefix = Binary (C23)
Common Memory Units
1 Byte = 8 bits
1 Kilobyte (KB) = 1024 bytes
1 Megabyte (MB) = 1024 KB
1 Gigabyte (GB) = 1024 MB
Bitwise Operations
Often used with hexadecimal numbers
Useful for:
- Flag manipulation
- Hardware interaction
- Memory optimization
- Bit masking

Common Use Cases

Decimal
General purpose calculations
User input/output
Mathematical operations
Octal
Unix file permissions
Legacy systems
Hexadecimal
Memory addresses
Color codes
Binary file formats
Network protocols
Debugging
Binary
Low-level programming
Hardware interfaces
Bitwise operations