Which base is associated with the hexadecimal number system?

Which base is associated with the hexadecimal number system?

• A. Binary Number System
• B. Decimal Number System
• C. Hexadecimal Number System
• D. Octal Number System

Answer: (C)

Bases in numeral systems determine how many distinct digits are available and how each position represents powers of the base. Hexadecimal uses sixteen symbols: 0 through 9 for values 0–9 and A through F for values 10–15. Because of this, its base is 16. The connection to computing comes from the fact that four binary bits (a nibble) correspond exactly to one hexadecimal digit (2^4 = 16), making it convenient to translate between binary and hex. For example, the binary sequence 1010 1111 converts to the hexadecimal A F, and FF hex equals 15×16 + 15 = 255 in decimal. Other common bases are binary (base 2), decimal (base 10), and octal (base 8).

Bases in numeral systems determine how many distinct digits are available and how each position represents powers of the base. Hexadecimal uses sixteen symbols: 0 through 9 for values 0–9 and A through F for values 10–15. Because of this, its base is 16. The connection to computing comes from the fact that four binary bits (a nibble) correspond exactly to one hexadecimal digit (2^4 = 16), making it convenient to translate between binary and hex. For example, the binary sequence 1010 1111 converts to the hexadecimal A F, and FF hex equals 15×16 + 15 = 255 in decimal. Other common bases are binary (base 2), decimal (base 10), and octal (base 8).