  In basic computational physics classes, students often raise the question of
how to compute a number that exceeds the numerical limit of the machine. While
technique of avoiding overflow/underflow has practical application in the
electrical and electronics engineering industries, it is not commonly utilized
in scientific computing, because scientific notation is adequate in most cases.
We present an undergraduate project that deals with such calculations beyond a
machine's numerical limit, known as arbitrary precision arithmetic. The
assignment asks students to investigate the approach of calculating the exact
value of a large number beyond the floating point number precision, using the
basic scientific programming language Fortran. The basic concept is to utilize
arrays to decompose the number and allocate finite memory. Examples of the
successive multiplication of even number and the multiplication and division of
two overflowing floats are presented. The multiple precision scheme has been
applied to hardware and firmware design for digital signal processing (DSP)
systems, and is gaining importance to scientific computing. Such basic
arithmetic operations can be integrated to solve advanced mathematical problems
to almost arbitrarily-high precision that is limited by the memory of the host
machine.
