Floating-point representations Consider the ANSI/IEEE short floating-point forma

Question

Floating-point representations Consider the ANSI/IEEE short floating-point format. Ignoring plusminus infinity, plusminus 0, NaN, and denormals, how many distinct real numbers are representable? What is the minimum number of bits needed to represents this many distinct values? What is the encoding or representation efficiency of this format? Discuss the consequences (in terms of range and precision) of shortening the exponent field by 2 bits and adding 2 bits to the significand field. Repeat part d, this time assuming that the exponent base is increased from 2 to 16.

Explanation / Answer

denoting a mode of representing numbers as two sequences of bits, one representing the digits in the number and the other an exponent which determines the position of the radix point.

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