Multiplying two N bit signed numbers together

[bd411]

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 ?

 

[lewando]

For 2's complement, this is true. For sign-magnitude, one less so.

 

[bd411]

That's pretty much the same thing that's bothering me... I have written the question as it has been asked. I'm assuming they mean sign magnitude ?

 

[lewando]

I suggest clarify question with instructor or state your assumptions in the answer. If you can't do that and if it is one of these computer-based answer entry systems (no assumptions permitted) I'd go with 2N. It allows you to do both.

 

[rcgldr]

For 2's complement, this is true. For sign-magnitude, one less so.

Or ones complement. For 3 bit sign-magnitude or one's complement numbers the range of products is limited to -9 to +9, which only requires 5 bits.