bit width for addition

[sky_above]

What will be the bit size required to do the addition where we add eight bits eight times. How to calculate that bit width in case of addition in binary?

 

[KlausST]

Hi,

Can´t you solve it on your own?

take a piece of paper and a pencil.
Then decide if you want signed or unsigned 8 bit representation.
Decide the highest absolute value.
Write this value 8 times among each other
calculate the sum.

The decide which bith width you need for this number.

********
mathematically:
* input_bit_width ( 8 bits)
* add_count (8)

output_bit_width = input_bit_width + log(add_count) / log(2)

Try both and see if both results match.
Decide why they don´t match exactly.

Klaus

 

[vGoodtimes]

The width is n lg n

 

[vGoodtimes]

--edit: n + lg