Question: Suppose you have a true random bit generator where each bit in the generated stream has the same probability of being a 0 or 1

Suppose you have a true random bit generator where each bit in the generated stream has the same probability of being a 0 or 1 as any other bit in the stream and that the bits are not correlated; that is the bits are generated from identical independent distribution. However, the bit stream is biased. The probability of a 1 is 0.5 + ∂ and the probability of a 0 is , where 0 < ∂ < 0.5 A simple deskewing algorithm is as follows: Examine the bit stream as a sequence of non-overlapping pairs. Discard all 00 and 11 pairs. Replace each 01 pair with 0 and each 10 pair with 1.

a. What is the probability of occurrence of each pair in the original sequence?

b. What is the probability of occurrence of 0 and 1 in the modified sequence?

c. What is the expected number of input bits to produce x output bits?

d. Suppose that the algorithm uses overlapping successive bit pairs instead of nonoverlapping successive bit pairs. That is, the first output bit is based on input bits 1 and 2, the second output bit is based on input bits 2 and 3, and so on.What can you say about the output bit stream?

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