Consider numbers having a binary representation consiting of aninfinite string o

Question

Consider numbers having a binary representation consiting of aninfinite string of the form 0.yyyyyy..., where y is a k-bitsequence. For example, the binary representation of 1/3 is0.01010101... (y = 01), while the representation of 1/5 is0.001100110011... (y = 0011). A. Let Y = B2Uk (y), that is, the number having binaryrepresentation y. Give a formula in terms of Y and k for the valuerepresented by the infinite string. HINT: Consider the effect ofshifting the binary point k positions to the right. B. What is the numeric value of the string for the following valuesof y? (a) 001 (b) 1001 (c) 00001111

Explanation / Answer

B. (a) 001

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