Floating point computation was in standard use by the mid 1950s. During the subsequent two decades, each computer manufacturer developed its own floating point system, leading to much inconsistency in how one program might behave on different machines. For example, although most machines developed during this period used binary floating point systems roughly similar to the one described in the previous chapter, the IBM 360/370 series, which dominated computing during the 1960s and 1970s, used a hexadecimal system (base 16). On these machines, the significand is stored using 24 bits, to be interpreted as 6 hexadecimal digits, leaving 1 bit for the sign and 7 bits for the exponent (representing a power of 16). Normalization requires only that the first hexadecimal digit be nonzero; consequently, the significand could have up to 3 leading zero bits. Therefore, the accuracy of the significands ranges from 21 to 24 bits; some numbers (such as 1/10; see (2.3)) are represented less accurately than on a binary machine. One motivation for this design was to reduce the bit shifting required during floating point add and subtract operations. Another benefit is that the hexadecimal base allows a much greater range of normalized floating point numbers than a binary system permits.

In addition to inconsistencies of representation, there were also many inconsistencies in the properties of floating point arithmetic. See Chapter 6 for examples of difficulties that could arise unexpectedly on some machines. Consequently, it was very difficult to write portable software that would work properly...