The paper is devoted to the synchronization problem of the discrete-time chaotic systems, coupled by the link (the communication channel) with the limited bit-per-step rate. The observer-based full-order coder is designed, ensuring decay of the synchronization error asymptotically for the case when channel imperfections and computation errors are neglected. It is shown that if the computations in the both master and slave nodes of the channel are identical, the synchronization error can be made close to the maximum achievable accuracy of the given computer depending only on the number of digits in the computer. If the calculations in the coder and decoder are not identical (e.g., if the computers on these nodes have different number of digits), after the some time interval of decreasing the synchronization error, the mis-synchronization occurs due to unstable properties of the chaotic systems. For this case, the practical synchronization may be ensured applying the fixed-point arithmetic calculations. The result is illustrated numerically on the example of synchronization chaotic Henon systems.