BINARY FLOATING-POINT NUMBERS
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Thus, the n bits that represent a floating-point number are partitioned into two parts, one holding the significand M and the other the exponent E. The range of representable floating-point numbers is larger than that of fixed-point representation, but the precision is smaller. The total number of different values (representable in n bits) is still 2n , and since the range between the smallest and the largest representable values increases, the distance between any two consecutive values must increase as well. Floating-point numbers are thus sparser than fixed-point numbers, resulting in a lower precision. Any real number whose value lies between two consecutive floating-point numbers is mapped onto one
of these two numbers. Therefore, a larger distance between the two consecutive numbers results in a lower precision of representation. A more detailed discussion on the precision of representation appears in Section 4.3.