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Uhh.. Yeah, thanks for that observation Captain Obvious....
That's not what he was asking. He's asking how did a mechanical cash register handle the math.
And the answer is, it uses a mechanical system to convert the numbers into binary numbers. Addition is relitivly simple. For subtractions, the binary number is inverted and added together (this is why it sounded like the mechanical cash register was going nuts when subtraction had to take place).
Example:
2=0010
1= 0001
0=0000
-1=1111
-2=1110
So, Someone walks up to the cash register with 2 dollars worth of stuff, gives the clerk 1 dollar, so they still owe 1 dollar. The cash register would perform this function:
0010+1111=10001 (drop the leading bit = 0001 or 1 dollar owed)
Only limitation is how large the coggs were.
There Ya go!