In digital electronics, three primary number systems are extensively used:
1. Binary (Base-2)
- This system uses only two digits: 0 and 1.
- Each digit represents a power of two, starting from 2<sup>0</sup> (1) for the rightmost digit.
- Example: The binary number 1011 is equivalent to (1 2<sup>3</sup>) + (0 2<sup>2</sup>) + (1 2<sup>1</sup>) + (1 2<sup>0</sup>) = 8 + 0 + 2 + 1 = 11 in decimal.
- Used for: Representing data within computers, communication between components, and logical operations.
2. Decimal (Base-10)
- This system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Each digit represents a power of ten, starting from 10<sup>0</sup> (1) for the rightmost digit.
- Example: The decimal number 123 is equivalent to (1 10<sup>2</sup>) + (2 10<sup>1</sup>) + (3 * 10<sup>0</sup>) = 100 + 20 + 3 = 123.
- Used for: Human interaction, representing quantities, and calculations.
3. Octal (Base-8)
- This system uses eight digits: 0, 1, 2, 3, 4, 5, 6, 7.
- Each digit represents a power of eight, starting from 8<sup>0</sup> (1) for the rightmost digit.
- Example: The octal number 123 is equivalent to (1 8<sup>2</sup>) + (2 8<sup>1</sup>) + (3 * 8<sup>0</sup>) = 64 + 16 + 3 = 83 in decimal.
- Used for: Representing memory addresses, simplifying binary numbers, and in some older systems.
While these are the most common systems, other bases like hexadecimal (Base-16) are also used in specific applications.
