1 Design a counter that produces the following count sequenc

1. Design a counter that produces the following count sequence:

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, · · · , 15, 15, · · · , 1, 2, 2, etc.

that is, it produces one 1, two 2’s, three 3’s, and so on, up to fifteen 15’s, after which it starts back with one 1, two 2’s, etc.

You have available a catalog of up counters and down counters, each with data inputs, load, enable, and clear inputs, and true and complemented form of each output. Assume that all counter inputs are active high.

Build a counter that realizes the above sequence by using only two counters from the catalog and no more than 10 logic gates (or, nand, nor, and, inverter). (Note: A solution is possible with significantly less then 10 logic gates.) Your answer should include a clear and neat circuit diagram, and an explanation of how your design works.

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