The correct answer is C. 63.
A 6-bit binary word can represent 2^6 = 64 different values. However, the first value, 000000, is used to represent the number 0, and the last value, 111111, is used to represent the number 63. Therefore, the maximum count which a 6-bit binary word can represent is 63.
Option A is incorrect because 36 is not a power of 2.
Option B is incorrect because 64 is the total number of values that a 6-bit binary word can represent, but the first and last values are not valid counts.
Option D
is incorrect because 65 is not a valid count for a 6-bit binary word.Option E is incorrect because C is the only correct answer.