In this research, we examine various problems which appear for the chaos modem system with finite bit length memory, and investigate measures to prevent degradation of chaotic nature. A chaos signal can show its original non-periodic random nature when it is expressed by a real number whose expression needs infinitely many digits. However, in practical engineering applications, in particular, for digital systems, a number is expressed naturally with finite digits. What kind of signal will appear when chaos is computed by finite digits? In general, when chaos is expressed by finite digits, it becomes a long periodic signal (this is called "pseudo chaos"). This pseudo chaos has properties similar to chaos within one period such that nearby orbits depend sensitively on initial conditions, and auto-correlation and cross-correlation functions tend to zero with time. From such properties we can realize a chaos modem system having some amount of security by synchronizing a pseudo chaotic transmitter and a pseudo chaotic receiver. We assume a practical 16 bit digital signal processor, and in the calculation, 32 bit accumulator is compressed into 16 bits via a certain method. We verify the randomness of the pseudo-periodic signal by using Diehard test which is proposed by a researcher in Florida State University. As a result, we have succeeded to obtain several parameter sets which have a good random nature.