Distribution densities of the mantissa and exponent of floating point numbers

The relations between the probability densities of real numbers and the corresponding mantissa and exponent densities in the floating point number format are investigated. Assumptions about continuity of the probability density of real numbers lead to certain restrictions in terms of the density of the mantissa. A few real number densities of practical importance were treated analytically and experimentally. During arithmetic operations like addition and multiplication which are essential for signal processing the operand density is altered. The effect concerning the densities of mantissa and exponent of the result is discussed. The reciprocal density of the mantissas plays a central role. Applications in roundoff-noise-analysis of signal processing with finite wordlength are considered