Question

What is the \(10\)'s complement of \((47)_{10}\)?

• A. 52
• B. 53
• C. 54
• D. 55

Hint:

10's complement of an n-digit number N is \(10^n-N\).

Answer 1

The Correct Option is B

Step 1: Recall the definition of the 10's complement.
For an $n$-digit decimal number $N$, the $10$'s complement is defined as \[ 10^n-N \] It is used in digital systems to carry out subtraction using addition.

Step 2: Find n for the given number.
$47$ has $2$ digits, so $n=2$ and $10^n=100$.

Step 3: Compute the 10's complement.
\[ 100-47=53 \]

Step 4: Check the other options.
$52$ is the $9$'s complement of $47$, found from $99-47=52$, not the $10$'s complement. $54$ and $55$ would come from an arithmetic slip such as adding an extra $1$ or $2$ after the subtraction.

Step 5: Final conclusion.
\[ \boxed{53} \]