Understanding Number Systems and Base 8

A number system is a way of representing numbers. Different number systems use different bases (also called radix) to count and represent values. The base of a number system determines the number of unique digits available in that system.

Let's look at the common number systems mentioned in the options:

• Decimal System: This is the number system we use in our daily lives. It has a base of 10. It uses ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• Binary System: This system is fundamental in digital electronics and computers. It has a base of 2. It uses only two unique digits: 0 and 1.
• Octal System: This system is sometimes used in computing as a compact way to represent binary numbers because 8 is a power of 2 ($$2^3=8$$). It has a base of 8. It uses eight unique digits: 0, 1, 2, 3, 4, 5, 6, and 7.
• Hexadecimal System: This system is also widely used in computing, especially for memory addresses and color codes. It has a base of 16. It uses sixteen unique symbols: 0-9 and A-F (where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15).

The question asks which type of number system is represented by base 8. Based on the definitions above:

• Decimal has base 10.
• Binary has base 2.
• Octal has base 8.
• Hexadecimal has base 16.

Therefore, the number system represented by base 8 is the Octal system.