Python3 check digit algorithm

Question

I'm learning to wrap my head around programming and have been given the following task:

The ISBN (International Standard Book Number) is made out of 10 digits.

z₁z₂z₃z₄z₅z₆z₇z₈z₉z₁₀

The last digit z₁₀ is a check-digit. It's made like this: First, you create a kind of cross-sum with this formula:

s = 1 * z₁ + 2 * z₂ + 3 * z₃ + 4 * z₄ + 5 * z₅ + 6 * z₆ + 7 * z₇ + 8 * z₈ + 9 * z₉

The check-digit z₁₀ is the remainder of the integer division of s divided by 11. For the remainder 10 you write x or X. Example: For the ISBN 3826604237 you get the check-digit 7.

Calculation: 1*3+2*8+3*2+4*6+5*6+6*0+7*4+8*2+9*3 = 150

The remainder of the division of 150 and 11 is 7.

The code-solution given is as followed:

# isbn.py
number = int(input("Please enter a 9-digit number: "))
z9 = number % 10
number = number//10
z8 = number % 10
number = number//10
z7 = number % 10
number = number//10
z6 = number % 10
number = number//10
z5 = number % 10
number = number//10
z4 = number % 10
number = number//10
z3 = number % 10
number = number//10
z2 = number % 10
number = number//10
z1 = number
sum = z1+2*z2+3*z3+4*z4+5*z5+6*z6+7*z7+8*z8+9*z9
checkdigit = sum%11
print("\nCheckdigit:", checkdigit)

My question simply is: How does it work? Why do I have to calculate "number // 10" and "number % 10" and this all the time? Is there a name for this kind of algorithm, and if so, how is it called?

I'd appreciate any kind of answer for this and if it seems like the easiest thing for you and you feel like I'm wasting your time, I'm sorry. So far I understood pretty much anything I've learned thus far learning python, but this task seemed a bit hard (it was in a very early chapter of the book I'm studying on work) and I got stuck and didn't get this out of my head.

Thank you in advance and have a nice day!

Answer 1

The operation x % 10 is called 'modulus' and returns the remainder of the division by 10. You use it in your code to isolate the rightmost digit.

The next operation x // 10 is called 'integer division', that is, a division which returns integers only (the fractional part (if any) is cut off). Integer division by 10 on a decimal number corresponds to a rightshift by one digit so that the next digit is shifted into the rightmost place.

You repeat these 2 steps until the last digit is isolated. Then you perform the multiplications, and finally take the modulus of 11 (the remainder of the division by 11) to obtain the check digit.

This repetitive code cries for a loop. Just imagine you had to handle 100 digit numbers.