Fixed-Point Arithmetic Modeled in B Software Using Reals

This paper demonstrates how to introduce a fixed point arithmetic in software developed with the classical B method. The properties of this arithmetic are specified with real numbers in the AtelierB formal tool and linked to an implementation written in Ada programming language. This study has been conducted to control the loss of precision and possible overflow due to the use of fixed point arithmetic in the critical software part of a communication based train control system.