Internal Representation

S/390 Floating Point

S	Exponent	Fraction
0	1-7	8 - end

The first bit indicates the sign of the floating point number. For short and long floating point numbers, the next 7 bits represent the exponent; the remaining bits represent the fraction as a binary number. The exponent value is increased by 64; thus exponents in the range -64 to +63 can be represented. A short floating point value is 4 bytes long; a long floating point value is 8 bytes long.

An extended floating point value consists of two 8 bytes values: the sign and exponent from the high order part are used for both; the fraction is the fraction from the high order part followed by the fraction from the low orderpart.

For example, the value 2.1 is represented as a short floating value as

x'41219999' which is x'219999'/x'1000000' or roughly 0.131249964 which is multiplied by 16 raised to the power 65-64 = 1 to give roughly 2.09999943.

IEEE Floating Point

S	Exponent	Fraction
0	1-8	9 - end

Again the first bit indicates the sign. The next 8 bits represent the exponent as a binary number. The exponent value is offset by 127; exponent values in the range -127 to +127 can be represented. Note that the exponent value 255 which would be equivalent to +128 is reserved for special values such as NaN (Not a Number). The remaining bits represent the fraction as a normalized value with the leading 1 removed.

For example, the value 2.1 is represented as a short floating value as

x'40066666' which is 1 + x'066666'/x'800000', roughly 1.049999952, which is multiplied by 2 raised to the power 128-7 = 1 to give roughly 2.099999904. See "IBM S/390 Support for IEEE Floating Point"