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It is necessary to synchronize the mutiplexer and demultiplexer in time division multiplexing because the multiplexor is encoding data onto the carrier at certain points in time. (This is why its called Time Division Multiplexing) The demultiplexor most know when the data of interest are present in the carrier, hence the need for synchronization. Note that there usually is a transmission delay between the multiplexor and demultiplexor. As a result, while the demultiplexor is in sync with the multiplexor, it is not necessarily in phase. The crucial point is that the data and clock be in sync and in phase at the demultiplexor.

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Q: Why is it necessary to synchronize mutiplexer and demultiplexer in time division multiplexing?
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