In a large communication network, there can be several different communication systems. When the systems having different digital representations are to be connected, there arise a code conversion problem. In this thesis work, the code conversion of $\mu$-law pulse code modulation (PCM) to and from adaptive differential pulse code modulation (ADPCM) has been studied. For the ADPCM system we have used an instantaneous companding adaptive quantizer and a fixed predictor. To estimate the performance degradation when code conversion systems are connected in tandem, a theoretical study has been done. The analytical results agree closely with computer simulation when RC-shaped Gaussian random signal was used as an input signal. In addition, hardware and software have been deisgned to realize the code conversion algorithm.