Real world example of error detection

ISBN
This is a international system used to identify books by a 10 or 13 digit number (including redundant bit). This system adds a  redundant bit  to the end of each of the code that is calculated using an specifically designed formula. This error checking is very similar to the parity cards both adding bits and using a formula. But with some errors there program used will have to check things apart from the check number, like there would have to be a catch for an invalid input of letters or to many/little letters

Error detection is used with the ISBN system because when someone is identifying details about a book in the ISBN data base, if they enter the number wrong and there is no error detection, they may think the data is missing. But because there is error detection, the program used will tell the user the number they entered may be wrong, so they could check and fix the number, or confirm the data is missing, or the book is fake. The program will determine if the check digit is correct, by calculating what the thirteenth digit should be,(using the formula) and what it actually is.

In the picture above, is me entering a random ISBN number into a simple program I made, to calculate what the check digit should be. In the case shown I entered 1436746842568, and for this code the check number should be 8, as its the 13th digit but it turned out to be 4, so in this example the error detection system was effective. I then did this another 29 times and 5 of the randomly chosen numbers matched their check number, this means, they prove that, the error checking system ISBN uses isn't perfect. So it is possible that a real books number could be entered slightly incorrect, and the programme would get a false result. The probability from the sample size of 30 is 1/6, so one in six is predicted to be incorrectly accepted by the error check system. But to comment on the probability of 1/6, I would have to say it is higher than I expected, and that is likely that, in a retest the number would have a considerable variation.

Common errors when typing out ISBN numbers, a lot of the time the user will make mistakes; this could be simple things like double tapping a letter by accident, pressing the number one above or below the one you are meaning to press, pressing a letter or other syntax. But these errors will be effectively detected with the check digit. In my opinion there aren't any ISBN number errors, that can't consistently be undetected.