Xerox/Scientific Data Systems Sigma 5 Numbers

These number representations are used for Xerox Data Systems (XDS), previously known as Scientific Data Systems, Sigma 5 computers.

These 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.  Negative floating point numbers are the two's complement of the positive representation.

SINGLE PRECISION is shown below:
 

Sigma 5 Floating Point Format
S	Exponent							Fraction
31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1	0

DOUBLE PRECISION adds another 32 bits of fraction in the following 32 bits.

NOTE that the Fraction, F, is

•     0 or 2^-24 <= |F| < 1 for single precision, and
•     0 or 2^-56 <= |F| < 1 for double precision.

Comparing numbers with many leading zeroes in |F| may lead to erroneous results.

INTEGER numbers are 32 bits long, and are in two's complement.