There isn't really (official) publicly available software to do this, but depending on the storage technology you can often tell not only the current binary state of a memory bit but also the previous one.

As an example, we might say a bit is on if it is at 5V and off at 0V. However, real bits have voltages that vary quite a bit and we just threshold at (say) 2.5V. The actual voltages depend on (among other things) the previous state of the bit. If AB denotes a previous state A and a current state B, you might have something like:

00 -> 0.5V 10 -> 0.9V 01 -> 4.1V 11 -> 4.5V

Note that is doesn't quite work like this. The main point is that with dedicated hardware you can try to read data that has been lightly overwritten. This is why tools intended to purge data will overwrite many times with random bit sequences to minimize the chance of data recovery.