Main circuit is the final result it works like Q*M 

this is a booth multiplication logic gate representation, booth multiplication is the fastest way to multiple binary number. Number of steps in booth multiplication are equal to the number of bits.

We are using a half adder to construct a full adder , full adder is used for making addition of two number(bits) possible. For addition of negative numbers we are using a airthmetic right shift to find the 2's complement and then perform normal addition.And according the value of Q0Q-1 we choose our output and update the input, after repeating the whole process four times we get the answer.

Then in a order to make one loop f booth algorithm 

And finally we append four loop to perform 4 loop booth multiplication as we are taking 4bit input