Color conversion between two encoding standards, sRGB and Internet FAX, is important for interchangeability and compatibility among Internet peripheral devices such as the monitor, printer, and FAX machine. To enhance the compatibility, we need to have the capability of converting between these color spaces accurately and cost effectively. To this end, we proposed a modular architecture for implementing this conversion via an internal exchange standard CIEXYZ.The implementation was simulated in software using floating-point and integer computations. Several integer implementations using lookup tables (LUT) were presented. The computational accuracy of integer implementations was examined and the comparison was made with respect to the floating-point computation. Finally, the optimal imaging path and bit-depth were recommended.