Computer number systems are fundamental to how computers represent and manipulate data. Here’s an overview of the most common number systems used in computing:

1. Binary Number System (Base-2):
   • Representation: Uses two digits, 0 and 1.
   • Usage: Fundamental in digital electronics and computing, where each bit (binary digit) represents a state of on (1) or off (0).
2. Decimal Number System (Base-10):
   • Representation: Uses ten digits, 0 to 9.
   • Usage: Commonly used by humans in everyday arithmetic and calculations.
3. Hexadecimal Number System (Base-16):
   • Representation: Uses sixteen digits: 0-9 followed by A-F (where A=10, B=11, …, F=15).
   • Usage: Compact representation of binary data and memory addresses, used extensively in programming and debugging.
4. Octal Number System (Base-8):
   • Representation: Uses eight digits: 0-7.
   • Usage: Rarely used now, historically used in computing for its compact representation of binary data.

Conversion Between Number Systems:

• Binary to Decimal: Convert each binary digit’s place value to decimal and sum them up.
• Decimal to Binary: Divide the decimal number by 2 repeatedly and record remainders.
• Binary to Hexadecimal/Octal: Group binary digits into sets of four (hexadecimal) or three (octal) and convert each group to the respective base.
• Hexadecimal/Octal to Binary: Convert each hexadecimal/octal digit to its binary equivalent.
• Decimal to Hexadecimal/Octal: Divide the decimal number by 16 (hexadecimal) or 8 (octal) and record remainders.
• Hexadecimal/Octal to Decimal: Multiply each digit by its base raised to the power of its position.

Understanding these systems is crucial for various tasks in computing, from programming and hardware design to data representation and networking protocols.