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## Homework Statement

Determine the number of bits needed to represent the range of results obtained when two N bit signed numbers are multiplied together.

## Homework Equations

None.

## The Attempt at a Solution

I considered the case when N = 3, i.e. a 3 bit signed number. The values that can be expressed with this are +3 - > -4. Hence with two 3 bit signed numbers we can get a maximum positive number of +16 and a maximum negative number of -12. We would therefore need 6 bits to represent this range of results (2N).

Looking at the case of 4 bits, the values that can be expressed are +7 -> -8. Here our largest positive number would be 64 and largest negative number -56. We would therefore need 8 bits (2N).

So my answer is 2N, is this correct ?