Question: (2) Consider numbers having a binary representation consisting of an infinite string of the form 0.yyyyy ..., where y is a k-bit sequence. For example,

(2) Consider numbers having a binary representation consisting of an infinite string of the form 0.yyyyy ..., where y is a k-bit sequence. For example, for example y = 01 gives the binary representation of , while the representation of is given by y = 0011. (a) Let Y = B2Uk(y), i.e. the number having binary representation y. Give a formula, in terms of Y and k for the value represented by the infinite string. (Hint: Consider shifting the binary point k positions to the right. If S were the value of the original string, what would the value of the shifted string be?) (b) What is the numeric value of the infinite) string for the following values of y? (A) 101 (B) 0110 (C) 010011
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