I am trying to design a sequential circuit that compute N! By consecutive multiplication method
I design overview of following circuit But I'm not sure about that .
what is your opinion ?

 

If I want to explain how it works and what the process is: first a number is loaded in the counter and with each clock, one unit is subtracted and then it is stored in the register(10bit) and the previous number is multiplied by the counter...
But I'm not sure Is the process correct or not. please guide me to complete it.

 

You have the basis
BTW: this is a clocked circuit , sequential tends to imply asynchronous. ( I know its technically not , but that's how the electronic industry is )

As this is home work, only a few pointers ?

How is the counter going to stop ?

When you load the counter, what happens to the number in the output register ?
will it not be the last number ?
why do yo need a clear into the counter ?

 

Now that I look at top circuit again, the middle one is typo and it is an multiplier , not an multiplexer.
When counter reached 0,then result is ready & it will stop & then clear.

 

This is the modified circuit...