Biased Exponents Encoding With Positive Zero When Comparing Absolute Values of Floating-Point Numbers
O. V. SAMOSHCHENKO, Irina Zeleneva, Heorhii Marhiiev, Oleksandr Miroshkin · 2020
Functional dependencies for determining of comparison flags for floating-point numbers modules have been formulated. Modified approaches for representation of floating-point numbers modules exponents are proposed, when exponents codes are proportional to their values. Mathematical dependencies for comparison flags calculation, represented as binary fixed-point codes, have been obtained. When comparing the values of floating-point numbers result of work is obtained both as relation between exponents and relative values of compared numbers fractions. Simplification of algorithm and its implementation in comparison circuits are achieved by joint and coordinated analysis of compared numbers fractions and exponents. That is why floating-point numbers representation method should be one, in which exponents and fractions could be represented as single binary polynomial, value of which is proportional to the numerical value of the floating-point code. To implement this exponent field should structurally become a part of fraction field and representation of a signed numbers should be proportional to its value. Application of 2's complement code for exponent representation does not fit this requirement, since complements codes of negative numbers as unsigned codes are greater than complement codes of its positive numbers. Exponent's biased code is proposed for using to fulfill the requirement.