(1) This problem considers numbers having a binary representation consisting of an infinite string of the...

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(1) This problem considers 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) [6] 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) [2] What is the numeric value of the (infinite) string for the following values of y? (1) This problem considers 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) [6] 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) [2] What is the numeric value of the (infinite) string for the following values of y?