Understanding 9's Complement Calculation

The 9's complement is a method used in digital electronics and computer science, primarily for representing negative numbers in older systems. For a decimal number, the 9's complement is found by subtracting each individual digit of the number from 9. This process applies to both the integer and fractional parts of the number.

Step-by-Step Calculation of 9's Complement

We need to find the 9's complement of the decimal number 782.54.

1. Identify the digits: The number 782.54 consists of the digits 7, 8, 2 in the integer part and 5, 4 in the fractional part.
2. Subtract each digit from 9:
   • For the integer part:
     • Digit 7: $9 - 7 = 2$
     • Digit 8: $9 - 8 = 1$
     • Digit 2: $9 - 2 = 7$
   • For the fractional part:
     • Digit 5: $9 - 5 = 4$
     • Digit 4: $9 - 4 = 5$
3. Combine the results: Assemble the calculated digits back into the number, maintaining the decimal point's position.
   • Integer part complement: 217
   • Fractional part complement: 45
   Combining these gives 217.45.

Final Result

Therefore, the 9's complement of the decimal number 782.54 is 217.45. This corresponds to option 217.45.