By James L. Peterson and Werner Rheinboldt (Auth.)
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Fixed-point or floating point? 3 THE INPUT/OUTPUT SYSTEM The largest memory unit and fastest computation unit in the world would be useless if there was no way to get information into the computer or to get results back from the computer. In fact, the usefulness of many present computers is severely limited by the way in which new programs and data can be put into and results displayed from the computer. Thus, the input/output (I/O) system is an integral component of a computer system. We will see that there exist a large number of radically different devices which the computer may use for this pur pose.
Zeros after the first nonzero digit can be significant. 1110000010 x 2~3. If we have only a limited number of bits to represent a floating point number, we want to store only the significant digits, not the leading zeros. This is accomplished by shifting our fraction and adjusting the exponent so that the first digit after the binary point is nonzero. This is the normalized form of a floating point number. Only zero has no one bits. It is treated as a special case with both an exponent and fraction of zero.
For - 1 3 (base 10), we have 110010 for a 6-bit representation and 111111110010 for a 12-bit repre sentation. Only the high order 6 bits differ between the 6-bit and 12-bit represen tations, and each of these bits is the same as the sign bit. If the quotient which results from a division exceeds the normal word length, it can be treated either as overflow or as a double-length quotient, according to how the computation unit is built. The remainder of a division by an n-bit divisor is never more than n-bits.