Question: 1. Consider a floating-point format that uses 8 bits of memory to store numbers: - 1 bit for the sign; - 3 bits for the

1. Consider a floating-point format that uses 8 bits of memory

1. Consider a floating-point format that uses 8 bits of memory to store numbers: - 1 bit for the sign; - 3 bits for the exponent; - 4 bits for the significand including the leading 1, i.e., significand is of the form (1.d1d2d3)2. (a) Compute fl(23.375), the floating point approximation of 23.375 using rounding. (b) To how many significant digits is fl(23.375) accurate? (c) When would you get numerical underflow and overflow errors with this format? Note that we are not dealing with a shifted exponent. (d) What is the largest integer M such that every integer between 1 and M are exactly represented by this format? (e) How many numbers can be represented exactly by this format? (a) Plot of g(x) and h(x). (b) Plot of f(x)=109x2e4x/5

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