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Number of states require to simulate a computer with memory capable of storing ‘3’ words each of length ‘8’.
(a) 3 * 2^8 (b) 2^(3*8)
(c) 2^(3+8) (d) None of the mentioned
Solution: Option (b)

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2 Answers

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Word size =8 bits

Number of words =3

so we need 24 bits to store these three words each of 8 bits.

Now these 24 bits can be set as 0 or 1 i.e. It can take 2^24 values . For each value we have a state corresponding to it  in  dfa so option b is correct.
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A better explanation here can be each state in a FSM can store one bit. So we need to find the number of bits required in this case. Consider the m words as segments of memory and each word is divided into n bits. So the total number of bits are m*n. And each bit can be in two states. Hence the answer is $2^{m*n}$.Hence the answer for this particular question is $2^{3*8}$

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