Resolution: The smallest detectable increment of measurement. Resolution is usually limited by the number of bits used to quantize the input signal. For example, a 12-bit A/D can resolve to one part in 4096 (2 to the 12 power equals 4096).
The above explanation of resolution is great. No, the resolution is not a function of scan time; however, some systems such as Direct Logic allow you to elect to convert @ a lower resolution to convert on every scan when you have multiple channels. Remember conversion time * # of channels would have to be less than scan time to assure a new conversion for all channels every scan. At times high bit count conversion take to long with short programs. I hope I didn't confuse the matter.
I would like to add that the resolution is a input module spec. so if the module 12 bit the resolution is 1/4096 as dbarid already explained, it may be some manufacturer have module that allows the user to set the resolution.
Assuming the module has a fixed resolution mean you have the value of your analog input stored in the module at this resolution.
The scan time is the time needed for the processor to read inputs, serve ports, execute the program and write the output.
Updating the analog value in the CPU has two main methods: (assume that you have one module with 8 inputs)
1- the CPU would update the 8 inputs each scan
2- the CPU would update only one input at each scan, so it will take 8 consecutive scans to update all inputs.
The draw back of the first one is the CPU would take considerable time to update all inputs hence the scan time will increase. The second method draw back is each channel would be updated every 8 scans.
Generally there is no connection between scan time and resolution
