These number representations are used for IBM 360/37/3081 numbers. IBM had earlier used 36-bit formats -- for the IBM 7094, for instance.
IBM floating point numbers are represented by one bit for the sign (S),
7 bits for the exponent, and 24 bits for the fraction. The exponent
is to the base 16 (not 2), and has a bias of 64. Because of the base
16, the fraction may have up to three leading zeros. In this manner,
some of the exponential value may be assumed by the fraction, increasing
its range, at the cost of some precision. Normalization to the leading
bit is not possible. Floating point numbers have no complement (neither
one's nor two's complement). They are in sign-magnitude format (the
sign being bit 31).
SINGLE PRECISION is shown below:
| IBM 32-Bit Floating Point Format | |||||||||||||||||||||||||||||||
| S | Exponent | Fraction (Note: the most significant three bits [23, 22, and 21] might all be zero). | |||||||||||||||||||||||||||||
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DOUBLE PRECISION adds another 32 bits of fraction
in the following 32 bits.
INTEGER numbers are in two's complement.