Practical 7

Exercise 1

It is easy to make a mistake typing a sequence of numbers. Many ID numbers include one or more "check digits" to help protect against typing errors. The digit(s) can be calculated in a number of ways.

One popular method involves the following steps,

1. the sum of the digits in the even positions
2. the sum of the digits in the odd positions
3. add three times the sum of the odd digits to the sum of the even digits
4. the remainder of this number when dividing by ten
5. subtracting this from nine gives the magic number

eg. calculate the check digit for the sequence 4561232

even sum: 3+1+5 = 9

odd sum: 2+2+6+4 = 14

combined sum: 3*14+9 = 51

remainder: 51%10 = 1

check digit: 9-1 = 8

The final number would then usually be written as 45612328 (10*4561232+8)

To get the digit in any position we can do an integer divide by 10^(col-1) and find the remainder when dividing by 10,

eg. find the digit in column 3 of the number 4561232,

divide by 10^(col-1) : 4561232 / 10^2 = 4561232 / 100 = 45612

find the remainder dividing this by 10 : 45612 % 10 = 2

• Write a function to find the digit at any position in an integer.
• Write a function to calculate the check digit for number of up to seven digits
• Write a function to confirm a check digit in an eight digit number

Exercise 2

• Modify the student database program to append a checksum when we first enter the student ID
• Extend the student database program to allow selection of students by entering their student ID, checking that the ID entered is typed correctly.