Comparator the number of bits resolution and step

[sunli567]

step size number of bits

Hi everyone,
I am preparing for analog CMOS design exam and meet a question about comparator.
Could you tell me the relationship between the number bits resolution and step size? The formula is best.
Thanks!

 

[sau_sol]

The theory is simple the more the number of bit the more precision you will get and the less the step size the more precision

hence they are inversely proportional

number of bits implies in how many bits the analog signal will consist of
and the step size will be used for quantization

like an 4 bit will resemble 2^4
and a step size 1 means it will have a total of 16 values
step size 2 means it will have a total of 8 values

like an 8 bit will resemble 2^8
and a step size 1 means it will have a total of 256 values
step size 2 means it will have a total of 64 values

 

[sunli567]

Thanks very much for your reply.

I still have below questions.
When i work out the number of steps, how can i know the number of bits needed?

For D/A linearity, it gives a point that 3 bit D/A need to set its levels to an accuracy of 1/65000. Why? In my opinion, it should be 1/8.