A systematic approach to synchronous time division multiplexing (TDM) in embedded systems employing TDM as a switching fabric in the form of a bus is presented. The benefits of this approach are increased system capacity, individual and unrestricted circuit creation for all channels regardless of their bandwidth, latency ranging from a fraction of a bit to several bits, and independent tracking of timing and control signals for all interfaces requiring such service. The method divides time in such a way that every circuit receives a quantum of time equal to its nominal bandwidth, thus allowing all circuits to be explicitly identified on the switching fabric. The procedure that accomplishes this type of TDM is based on solutions to sets of linear congruences, also known as linear Diophantine equations. This scheme significantly reduces the cost of an embedded interface and allows flexibility for unbundling the subrate channels, thus permitting easy implementation of subrate multiplexing. It also simplifies design of switching fabrics which must carry voice mixed with subrate bit-interleaved or packet mode data and with ISDN nodes.>