two 4bit no. when multiplied results in max no. of 1s

[pooja_khubbar]

hello friends
can anyone tell me two 4bit numbers....whose multiplication leads to maximum no of 1s in output.

 

[betwixt]

14 x 9 = b'1111110' ? That gives 6 ones.

Brian.

 

[lostinxlation]

well, your question is incomplete, but at my full discretion to expand your question, I'd say you can get as many 1s as you want by 1111 x 0001. You can get 7 1s, a million 1s or whatever number of 1s you want.

 

[betwixt]

I overlooked the obvious and yes @lostinxlation you are correct. I assumed the question referred to two 4-bit numbers and an 8-bit answer. The size of the result wasn't specified, your answer is correct for a 4-bit result. It's an interesting question though, I wonder if there is a mathematical formula for maximizing the number of ones in a number when it is the product of two smaller ones. I'n not sure if it would have a practical application, pehaps in parity generating/checking routines.

Brian.

 

[lostinxlation]

your answer is correct for a 4-bit result.

actually, it doesn't matter how many bits the result is expected with. The result of 1111 x 0001 would be full of 1s without 0s regardless of the expected bit width of the result in a certain case. THe problem is OP didn't ask the question properly and both of your answer and my answer are correct, depending on numbering system.

Since I think this is a homework or some assignment, I didn't elaborate it, but I'm sure you understand what I mean by 'numbering system'.

 

[FvM]

The result of 1111 x 0001 would be full of 1s without 0s regardless of the expected bit width

It seems to me, that signed or unsigned multiply should be specified first.

 

[pooja_khubbar]

thanks all..for the reply..in my case am taking unsigned no.... and its not a homework or assignment..am trying to design some multipliers and then i ve to evaluate the performance of dyanmic ckt..and am using simple binary no.s