In accordance with the principles of this invention, Pulse Code Modulation (PCM) signal streams are converted into Asynchronous Transfer Mode (ATM) cells for switching and transmission across a telecommunications network. Each cell carries one PCM sample of up to 48 different voice connections, the voice connections selected from the PCM data streams because they have a common destination. The cells are transmitted over ATM virtual circuits, each circuit transmitting one cell every 125 .mu.s. Advantageously, ATM transmission systems interface with PCM systems without adding appreciable delay and without requiring additional buffering. Advantageously, new voice paths can be established most of the time by using available slots in the cells of existing virtual paths. This application relates to arrangements for converting the PCM signal streams into ATM cells.