For a binary up/down counter with synchronous clear and preset , my question is what is the exact function of the preset here ? I have done many searches but every source assumes that the reader knows what is the preset function is and just mentions that the counter does have a preset input.
Since you mentioned "synchronous clear and preset", they are no different from any other counter control or counter data signals. They all traverse through combinational cloud, and finally converge at the D pin of several flip-flops. From the perspective of circuit, synchronous clear or preset are just DATA. We human beings call them clear or preset signal just because they do the clear or preset job functionally. So this is not an essential issue.