By rewriting the number in an exponent form, it isoften much easier for the computer to manipulate; but,as noted, we give up the digits that were rounded. As aresult, some resolution (the number of digits in thefraction) is usually lost.For instance, the number325786195 could be expressed as 3.26 × 10^{8 }or.32579 × 10^{9}.Still, this concept is useful. Thecomputer, however, is limited by the hardware in thenumber of bits its registers and memory cells canaccommodate.FLOATING-POINT FORMAT.— The formatfor the characteristic and mantissa during floating-pointoperations will vary with the register size. However,the binary (radix) point is usually located between thesign bit and the msb of the mantissa. Typically,floating-point numbers use a 32-bit word size. Let’sillustrate a couple of examples—one with a fractionalnumber and another with a very large number. Refer tofigure 5-15, frames A and B, during our discussion.We use one’s complement in our examples with32-bit size words. We’ll use the number 6.54321^{8 }asour example of a fractional number (fig. 5-15, frame A).Our fractional number will require two 32-bit words. Inthis case, notice the integral characteristic can have amaximum positive or negative value of 2^{15 }minus 1 andcomprises the least significant 16 bits of the word. Bit15 contains the one’s complement sign, which isextended through the most significant 16 bits of theword. The mantissa is the fractional part of the numberand is processed as a 32-bit number including the sign.Figure 5-15.—Floating-point numbers: A. Fractional number; B. Very large number.5-21

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