To secure the 64 kbps clear channel capability in the ISDN, it was decided to convert its North American digital transmission system into the European system especially in DS1 level. But their different companding law became an issue in the process of R&D in the existing time division digital switch such as TDX-1 to incorporate it into the ISDN. TDX-1 has been installed with North American ${mu}$ companding law and its ISDN capability is under development now. Thus, because of the ${mu}$ law/A law conversion for the interworking of two different transmission system, it is difficult to maintain the ISDN B channel transparency between TDX-1 and new European system with A companding law. Among some solutions for it, European frame format with ${mu}$ law companding is recommended. Those problems and solutions are presented in this paper.