although the computer represents the exponent in base 2 as well as the rest of the number, to simplify the notation we show the exponent in decimal.a standard scientific notation for reals in normalized form offers three advantages. It simplifies exchange of data that includes floating point number: it simplifies the floating-point arithmetic algorithms to known that numbers will always be in this form. and ot oncreases the accuracy of the number that can be stored in a word, since the unnecessary leading 0s are replaced by real digits to the right of the binary point.Floating point representition.a designer of floating point representation must find a compromise between the size of the fraction and the size of the exponent, because a fixed word size means you must take a bit from one to add bit to the other. This tradeoff is between precision and range; Increasing the size of the fraction enhances the precision of the fraction, while increasing the size of the exponent increases the range of the number thar can be represented. As our design guideline from chapter 2 remind us. good design demand good compromise.Floating=point number ars ussualy a multiple of the size of a word. The represetation od a MipS floaring -point number is show below, where is the sign of the floating -ponit number(1 meaninf negative) exponent is the value of the 8 bit exponent field and fraction is the
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