How to convert voltage into digital signals?
In general what you are looking for is a analog to digital converter, or A/D for short.  There are many different types.  Each different technology has its own tradeoff between speed, accuracy, resolution, cost, and other parameters.

One method of making a number from a analog parameter is to have the parameter change the frequency of a oscillator as it seem you did with your 555 timer, then measure the frequency.  There are many other ways too.  Nowadays, just about every microcontroller comes with a A/D converter built in.  10 bits is quite common.  Some low end ones may only have 8 bits, and 12 bits is available too.  Beyond that the anlog requirements get difficult to meet with the same technology the micro is fabricated with, so you pretty much need a external A/D for more than 12 bits.

The battery in your UPS may be isolated from the output or not at the same ground reference, so some care must be taken to measure its voltage and get the data into your PC.  My first knee jerk reaction is to put a small micro on the battery circuit.  It measures the battery voltage locally, then sends the resulting digital data serially over a single opto-coupler to another micro that interfaces to the PC via USB, or perhaps directly to the PC's COM port.