Making a 4 bit multiplier from 4 bit adders and AND gates

[cupparamen]

Hi,

Before I state the question I'm having trouble with, I want to say I'm a first year university (college) student who
has just been introduced to binary/logic circuits. I hope you'll be able to explain to me in a VERY basic way.

Question:
Sketch a combinational circuit which takes as input, two 4-bit binary numbers, A3,A2,A1,A0 and B3,B2,B1,B0, and
which outputs the 8-bit product P7,P6,P5,P4,P3,P2,P1,P0. Assume that you have available sixteen 2-input AND gates
and three 4-bit adders. Please explain the reasoning behind your design.
The circuit symbol for the 4-bit adder is shown in Figure 1. Note that C0 is the carry-in and C4 is the carry-out.

From what I understand, multiplication in binary would be something like, if B0 is 1, you take A3,A2,A1,A0 as an
input. If B1 is 1, you take A3,A2,A1,A0,0 and add it to what you got from the previous step. And so on. If any of
the B values are 0 you take all 0's. Still I don't understand how to do this at all. I would really appreciate an answer
at this point as I have been working on this problem for a day, searching the internet and I had no progress at all.
If it's possible please draw the circuit. It would be much much appreciated.

Thanks very much.

 

[aruipksni]

x3 x2 x1 x0
x
y3 y2 y1 y0
==============================
0 x3&y0 x2&y0 x1&y0 x0&y0
+ 0 x3&y1 x2&y1 x1&y1 x0&y1
+ 0 x3&y2 x2&y2 x1&y2 x0&y2
+ x3&y3 x2&y3 x1&y3 x0&y3
==============================

so you have and gates and 4 bit addres - now finish the job ...