To solve this question, the user needs to know the concept of binary number representation and the parity of numbers.

In binary number representation, each digit can only be 0 or 1. The rightmost digit represents $2^0 = 1$, the second rightmost digit represents $2^1 = 2$, the third rightmost digit represents $2^2 = 4$, and so on. To get the decimal equivalent of a binary number, we add up the values of the digits that have a value of 1.

For the binary number 10111001, the decimal equivalent is:

$1\times2^7 + 0\times2^6 + 1\times2^5 + 1\times2^4 + 1\times2^3 + 0\times2^2 + 0\times2^1 + 1\times2^0$

$= 128 + 0 + 32 + 16 + 8 + 0 + 0 + 1$

$= 185$

To determine if 185 is an odd number, we can check if it is divisible by 2. If it is not divisible by 2, then it is an odd number.

185 is not divisible by 2, therefore it is an odd number.

The Answer is: A