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Signed binary numbers multiplication

Hello to everyone,

I have to draw a logic circuit with the above data:

Input: 2 two-bit signed binary numbers in two's complement format. (eg A(a1a0) and B(b1b0))
Output: a number Z (in two's complement format, also). Z= AxB (multiplication) if at least an input number is negative. In any other case Z = A + B (addition)

I'm trying to find what is the min amount of bits for the output.

So, if the input is A=10 and B=10, we have output Z = 0100. So, I think that the output should be 4bit (in two's complement) binary number.

Am I on the right direction?
 
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