The single precision IEEE FPS format is composed of 32 bits, divided into a 23 bit mantissa, M, an 8 bit exponent, E, and a sign bit, S:
The normalized mantissa, m, is stored in bits 0-22 with the hidden bit, , omitted. Thus M = m-1.
The exponent, e, is represented as a bias-127 integer in bits 23-30. Thus, E = e+127.
The sign bit, S, indicates the sign of the mantissa, with S=0 for positive values and S=1 for negative values.
Zero is represented by E = M = 0. Since S may be 0 or 1, there are different representations for +0 and -0.
The maximum value of E = 255 is reserved to indicate overflow values (usually the result of floating point arithmetic) with exponents that are too large or too small to be represented.
The special interpretations for E = 255 and M = 0 are for S = 0 and for S=1. Floating point division by zero produces a number with E=255 and nonzero M called NaN (Not a Number).
To convert decimal 17.15 to IEEE FPS:
The hexadecimal value is 0x41893333.
The range of values for the mantissa, m, is between 1 and 2- .
Because E=0 and E=255 are reserved, the range of values for the exponent, e, is between -126 and +127.
The largest positive number that can be represented is approximately The decimal value of this number is approximately since
The mantissa represents a 24 bit binary fraction which corresponds to approximately 7 decimal digits since