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Assume that we have the following 32 bit floating point value:

0100 | 0000 | 0100 | 1001 | 0000 | 1111 | 1101 | 1011
^ ^
Bit 31 Bit 0

For simplicity's sake, the Hex representation of this value is 40490FDB. Using the IEEE 32 bit floating point definition, the mantissa is 490FDB (bits 22 through zero); the exponent is bits 30 through 23 (10000000) which is the Hex value of 80; and the sign (bit 31) is zero, which means it is positive.

For the 8087 math co-processor, the exponent has an assumed one, thus 80 + 1 = 81 which is 129 decimal. The real exponent is 129 minus 128 which is 1. This value of 1 is raised by the power of two and the resulting value (21 = 2) is used to multiply the mantissa with.

The mantissa is 490FDB which is a 22 bit number that represents the range from one to two. Thus, 490FDB is normalized by dividing it by 800000 (Hex) which is .570796 (decimal). Since the normalization bit is omitted, we add 1 to .570796 and get 1.570796. Multiply 1.570796 by 21 and we get 3.14159.

This turns out to be the value of Pi (p). Thus, the 32 bit floating value shown above (40490FDB Hex) is the IEEE 32 bit floating point format of Pi!

You can verify this with the following line in C:

float f=3.1415926535; printf("%IX",*(long*)&f);

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