Optimal finite bit Pi representation

Abstract

In this paper an optimal finite bit representation of Pi is presented. The goal is to completely nullify the possibility of error arising due to finite bit Pi representation while converting angle from degree (fixed point) to radian (IEEE 754 Single Precision floating point). Such a conversion is widely used in FPGA based interfacing device for military and aerospace applications, where there is minimal tolerance for error in the system. Through CAD based approach it is determined that atleast 40 bits are required to represent Pi while converting angle from 16 bit degree in 2's complement to IEEE 754 Single Precision floating point radian. © 2014 IEEE.