1. Consider the set of binary floating point numbers x that have 4 binary digits of...

 

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1. Consider the set of binary floating point numbers x that have 4 binary digits of precision: Here = x= x 2. 1, e is an integer, and x = 1.aa2a3 is a binary fraction having precision of 4 binary digits such that (1)2 < < (10) 2. (a) How many such floating point numbers x are there such that 1 < x < 2? (Here x is supposed to have 4 binary digits of precision.) List them: (b) How many such floating point numbers x are there, such that 1/2 < x < 1? (c) How many such floating point numbers x are there, such that 2 < x < 4? (d) What do you conclude about the density of the distribution of floating point numbers (in general) at smaller versus bigger magnitudes? 1. Consider the set of binary floating point numbers x that have 4 binary digits of precision: Here = x= x 2. 1, e is an integer, and x = 1.aa2a3 is a binary fraction having precision of 4 binary digits such that (1)2 < < (10) 2. (a) How many such floating point numbers x are there such that 1 < x < 2? (Here x is supposed to have 4 binary digits of precision.) List them: (b) How many such floating point numbers x are there, such that 1/2 < x < 1? (c) How many such floating point numbers x are there, such that 2 < x < 4? (d) What do you conclude about the density of the distribution of floating point numbers (in general) at smaller versus bigger magnitudes?