Which numbering system uses powers of 16 and digits 0-9 and A-F?

Which numbering system uses powers of 16 and digits 0-9 and A-F?

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

Answer: (D)

This question tests knowledge of base numbering systems. The system that uses base 16 and includes digits 0–9 plus letters A–F is hexadecimal. In hex, each position represents a power of 16, so the rightmost digit is 16^0, the next is 16^1, and so on. The symbols cover 0–9 for values zero through nine, and A–F for ten through fifteen. For example, 2AF hex equals 2×16^2 + 10×16^1 + 15×16^0 = 2×256 + 160 + 15 = 687 in decimal. Other bases use different symbol sets: binary uses only 0 and 1 (base 2), octal uses 0–7 (base 8), and decimal uses 0–9 (base 10). Hex is widely used in computing because it maps neatly to binary data and is convenient for representing memory addresses and color codes.

This question tests knowledge of base numbering systems. The system that uses base 16 and includes digits 0–9 plus letters A–F is hexadecimal. In hex, each position represents a power of 16, so the rightmost digit is 16^0, the next is 16^1, and so on. The symbols cover 0–9 for values zero through nine, and A–F for ten through fifteen.

For example, 2AF hex equals 2×16^2 + 10×16^1 + 15×16^0 = 2×256 + 160 + 15 = 687 in decimal.

Other bases use different symbol sets: binary uses only 0 and 1 (base 2), octal uses 0–7 (base 8), and decimal uses 0–9 (base 10). Hex is widely used in computing because it maps neatly to binary data and is convenient for representing memory addresses and color codes.