# utilize a single channel to transmit data generated from 16 users (using mux)

I have found this question in a book and find it confusing. The question is,

For a communication system, it is required to utilize a single channel to transmit the data generated from 16 users. Design a feasible circuit to aggregate the 16 users to a single channel using 4:1 multiplexers. Design a user selection circuit to interface with the above designed aggregation circuit. Please help me get an answer for this with explanation.

On the left, I've used 2:1 muxes and then boxed them together to create a bigger 4:1 mux. Using this construction method of building larger muxes from smaller muxes you can construct your 16:1 mux. As shown in the schematic, the dashed boxes represent a 4:1 mux, so only 5 4:1 muxes are necessary to construct your 16:1 mux; 4 on the bottom layer and one for the top layer. The key insight is to build them using a tree structure. Also, each 4:1 mux requires two select bits, one bit for each layer of the mux tree. I will leave it to you to design the larger 16:1 mux select circuit. Hint: each layer requires two bits! For example lets say we want to select user #10 (with user #0 at the top): our select line would be a 4-bit bus with value 0101.
• I've updated my answer with an example to select user #10. So there would be a two-bit bus going to the first layer of 4:1 muxes then another 2-bit bus going to the second 4:1 mux layer. Only two selectors, each 2-bits. – dopamane Oct 6 '18 at 7:15