Question

Convert a decimal number 3509.14453125 into a hexadecimal number

• A. DB5.25
• B. 437.1121
• C. 10110.11011
• D. AB6.456B

Hint:

Integer part conversion (Decimal to Hex): Repeatedly divide by 16, collect remainders in reverse order. (Remainders 10-15 are A-F).
Fractional part conversion (Decimal to Hex): Repeatedly multiply the fractional part by 16, collect integer parts in order.

Answer 1

The Correct Option is A

To convert the decimal number 3509.14453125 into a hexadecimal number, follow these steps:

1. Convert the integer part (3509) to hexadecimal:
   Divide the integer by 16 iteratively, recording the remainder at each step.
   • 3509 ÷ 16 = 219 R 5 (Remainder)
   • 219 ÷ 16 = 13 R 11
   • 13 ÷ 16 = 0 R 13
   Write the remainders in reverse order: D (13), B (11), 5. Therefore, the integer part in hexadecimal is DB5.
2. Convert the fractional part (0.14453125) to hexadecimal:
   Multiply the fraction by 16, take the integer part, and repeat.
   • 0.14453125 × 16 = 2.3125 (Take 2)
   • 0.3125 × 16 = 5.0 (Take 5)
   The fractional part in hexadecimal is .25.
3. Combine the results:
   The conversion of 3509.14453125 into hexadecimal is DB5.25.