Could thermostats be designed to work with half degrees?

It's often difficult to achieve the comfortable spot in the case of an air conditioner. A common problem is for one temperature to be too warm while the next degree below it is too chilly. Thermostats don't have full precision, so the state of indoor air can slightly fluctuate before a compressor makes a change. Would it be possible to increase the sensitivity of the computers than run temperature gauges so that half degrees could be acknowledged? If so, then air conditioning compressors would also need to be redesigned to withstand the more frequent and increased energy demand.

An old timer told me when I was young, we can make anything possible, if you have enough money. Of course there are devices sensitive enough to achieve very precise levels of accuracy. Your consideration for the device that disperses the heat outside is very perceptive. In the case of .5 degrees of accuracy you may find the unit doing the cooling (the compressor) may need to run 24/7, or you may need to install a parallel unit, of lesser size to maintain. Either way you electric bill will reflect the convenience, the systems you are recommended are designed to run for these extended periods.

Thank you keeseguy, for your reply and the compliment. Since the compressor of an air conditioner needs to have chances to turn itself on and off regardless of accuracy, the computer operating it would have to be programmed to treat and allow the action the same way. It would just have to be capable of doing so at the points of half degrees instead of whole ones. Anyone who were able to get such an air conditioner would need separate thermostats for the said unit and a heater. A house would get unbearably hot if its heater didn't have a numerical curve, and work of that frequency would quickly destroy a boiler or heating pump as its delivery only functions on the automatic setting.