After Her Majesty required some service time out of me I worked for a computer company and apart from the binary system we expressed 6 bit numbers in Octal (base 8) then the French landed us with a machine that counted 4 bit numbers as 1-2-4-(minus 2) can you believe it!
On the way to reduce the number of cycle times to do a multiplication we had what was referred to as the Russian method. This involved the Multiplicand being doubled as the Multiplier was halved and the odd answers stored to be added later.
Visualising this when fault finding was strangely satisfying, this went on for many years until computers started to assess faults with in themselves and as long ago as 1980.
It was attending a computer fault where a standard computer had an extended mathematical unit connected (it was calculating stresses for London Bridge which was undergoing repairs at the time).
Instructions were to press an otherwise indicator button, a stream of characters was printed out and these were used to trace a Q & A path through the associated book and it indicated which PCB was at fault, it was replaced and the computer was fixed. The unit used high-level mathematical functions using Floating Point arithmetic. No! I did not understand it either!.
I moved a bit up and a bit on after that experience.
Roy