To convert an octal number to a binary number, we need to convert each digit of the octal number into a 3-bit binary number.

Given octal number: (471)8

Step 1: Convert each digit of the octal number into a 3-bit binary number.
- Digit 4: (100)2
- Digit 7: (111)2
- Digit 1: (001)2

Step 2: Combine the binary numbers obtained from each digit to get the equivalent binary number.
- (100)2 + (111)2 + (001)2 = (100111001)2

Therefore, the octal number (471)8 is equivalent to the binary number (100111001)2.

Explanation:

The octal number system uses a base of 8 and has digits ranging from 0 to 7. Each digit in the octal number represents a power of 8. In contrast, the binary number system uses a base of 2 and has digits ranging from 0 to 1. Each digit in the binary number represents a power of 2.

To convert an octal number to a binary number, we need to convert each digit of the octal number into a 3-bit binary number. This is because 2^3 = 8, so each digit in the octal number can be represented by a 3-bit binary number.

In this case, the octal number (471)8 has three digits: 4, 7, and 1. We convert each of these digits into a 3-bit binary number:

- Digit 4: (100)2
- Digit 7: (111)2
- Digit 1: (001)2

Then, we combine the binary numbers obtained from each digit to get the equivalent binary number:

(100)2 + (111)2 + (001)2 = (100111001)2

Therefore, the octal number (471)8 is equivalent to the binary number (100111001)2.

Hence, the correct answer is option 'C' - (100111001)2.