5. The telephone numbers in a town run from 00000 to 99999. There are a number of errors that commonly occur The Diagonal Error: a common error in dialling on a standard keypad is to punch in a digit diagonally adjacent to the intended one. So on a standard dialling keypad, 4 could erroneously be entered as 2 or 8 (but not as 1, 5, or 7). 023 230 o The Switch Bug: After a correct number has been called in transmission, one pair of adjacent digits gets swapped. For example the number abcde could be called but whoever is at abced receives the phone call. The Smudged Digit: A single digit gets compted in transmission and it is known which digit got corrupted. For example: 38754 is dialed but in transmission, it becomes 38704. The Digit Error: A single digit gets changed into another random digit during transmission and it is unknown which digit was changed. For example 38754 is dialed but 38757 receives the call. It has been decided that a sixth digit will be added to each phone number. Given a phone number abcde, there are three different proposed schemes: Code 1: a+b+c+d+e+X = 0 (mod 10) Code 2: 2a +b +2c + d + 2e +X = 0 (mod 10) Code 3: 6a + 5b + 4c + 3d + 2e +X = 0 (mod 10) Fill out the following chart with a Yes or a No (you do not have to show your work). Can detect a Can detect a Diagonal Error? | Switch Bug? Can correct a Can detect a Smudged Digit? | Digit Error? Code 1 Code 2 Code 3 5. The telephone numbers in a town run from 00000 to 99999. There are a number of errors that commonly occur The Diagonal Error: a common error in dialling on a standard keypad is to punch in a digit diagonally adjacent to the intended one. So on a standard dialling keypad, 4 could erroneously be entered as 2 or 8 (but not as 1, 5, or 7). 023 230 o The Switch Bug: After a correct number has been called in transmission, one pair of adjacent digits gets swapped. For example the number abcde could be called but whoever is at abced receives the phone call. The Smudged Digit: A single digit gets compted in transmission and it is known which digit got corrupted. For example: 38754 is dialed but in transmission, it becomes 38704. The Digit Error: A single digit gets changed into another random digit during transmission and it is unknown which digit was changed. For example 38754 is dialed but 38757 receives the call. It has been decided that a sixth digit will be added to each phone number. Given a phone number abcde, there are three different proposed schemes: Code 1: a+b+c+d+e+X = 0 (mod 10) Code 2: 2a +b +2c + d + 2e +X = 0 (mod 10) Code 3: 6a + 5b + 4c + 3d + 2e +X = 0 (mod 10) Fill out the following chart with a Yes or a No (you do not have to show your work). Can detect a Can detect a Diagonal Error? | Switch Bug? Can correct a Can detect a Smudged Digit? | Digit Error? Code 1 Code 2 Code 3
