I have an assignment that requires building 4-bit Multiplier in two ways:

1) using only FA1bit and AND logic gates.

2) using only FA8bit(Full adder for 8bit numbers) , Mul2bit(Multiplier for numbers with 2 bits) and AND logic gates .

i figured out the first way , but i cant figure out how to do the second way .

(of course im talking about binary numbers)



You need to think about how you multiply decimal numbers by hand.

Now, think of your two 4-bit binary numbers as being written in base 4.

Do you see the analogy? Do you see how 2-bit multipliers might apply?

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    \$\begingroup\$ so let's say i have ABCD , XYWZ are four bit numbers . i can take AB , CD , XY and WZ to be numbers in base 4 since the maximum number can be 11 which is a single digit in base 4 . and then the result would be ABXY + ABWZ +CDXY +CDWZ ? \$\endgroup\$ – Mahmoud Qahawish Dec 20 '15 at 2:46
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    \$\begingroup\$ Yes, but with the partial products shifted by appropriate amounts before adding them together. \$\endgroup\$ – Dave Tweed Dec 20 '15 at 2:51

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