Multiplication of two number in 2's complement

Question

Suppose that we have two n bit, binary numbers in 2'th complement. If we multiply them the result needs less than 2n bits except in one state result needs 2n bit.

What is that state?

Answer 1

I guess it is when you multiply the smallest negative number by itself. For example, with $2$ bits: $10\times 10=0100$ (i.e. $(-2)\times(-2)=4$) and you really need the leading zero to express the fact that the result is positive.