Calculate 11024\(_5\) - 3220\(_5\).
Explanation
To solve \(11024_5 - 3220_5\), follow these steps:
Step 1: Convert the base 5 numbers to base 10.
1. Convert \(11024_5\) to base 10:
\[
11024_5 = 1 \times 5^4 + 1 \times 5^3 + 0 \times 5^2 + 2 \times 5^1 + 4 \times 5^0
\]
\[
= 1 \times 625 + 1 \times 125 + 0 \times 25 + 2 \times 5 + 4 \times 1
\]
\[
= 625 + 125 + 0 + 10 + 4 = 764_{10}
\]
2. Convert \(3220_5\) to base 10:
\[
3220_5 = 3 \times 5^3 + 2 \times 5^2 + 2 \times 5^1 + 0 \times 5^0
\]
\[
= 3 \times 125 + 2 \times 25 + 2 \times 5 + 0 \times 1
\]
\[
= 375 + 50 + 10 + 0 = 435_{10}
\]
Step 2: Subtract the base 10 numbers.
\[
764_{10} - 435_{10} = 329_{10}
\]
Step 3: Convert the result back to base 5.
\[
329_{10} = 4 \times 5^3 + 2 \times 5^2 + 3 \times 5^1 + 4 \times 5^0
\]
\[
= 4 \times 125 + 2 \times 25 + 3 \times 5 + 4 \times 1 = 11024_5 - 3220_5 = 2304_5
\]
The correct answer is A. 2304\(_5\).