What is the 15's complement of the hexadecimal number (C00D0)16?

Concept

For an n-digit hexadecimal number, the 15's complement is formed by replacing every digit d with F − d, where F represents 15.

This digitwise rule makes each original digit and its complement add to F without carrying to an adjacent position.

Application

1. For the first digit C: F − C = 3.

2. For each zero: F − 0 = F.

3. For the digit D: F − D = 2.

4. For the final zero: F − 0 = F.

5. Keeping the original order gives (3FF2F)16.

Cross-check

Adding the original number and the complement gives (C00D0)16 + (3FF2F)16 = (FFFFF)16; every position sums to F, confirming the result.