Append a check digit to 45723
Answers
Above question is incomplete and complete question is reas as:
Use the Verhoeff check-digit scheme based on D5 to append a check digit to 45723.
Answer:
The check digit for the number 45723.
Step-by-step explanation:
The Verhoeff check-digit scheme is a method for appending a check digit to a given number to detect errors in data entry or transmission. It is based on the concept of permutation and multiplication in a special table called the D5 table.
To append a check digit to the number 45723 using the Verhoeff scheme, follow these steps:
Step 1: Create the D5 table
The D5 table is a 5x5 table with unique digits arranged in a specific pattern. Here is the D5 table:
0 1 2 3 4
1 2 3 4 0
2 3 4 0 1
3 4 0 1 2
4 0 1 2 3
Step 2: Reverse the number
Reverse the digits of the given number 45723 to get 32754.
Step 3: Initialize variables
Set the variables checksum and digit to 0.
Step 4: Perform the calculation
Starting from the rightmost digit of the reversed number, perform the following operations:
For each digit in the reversed number, retrieve the corresponding digit from the D5 table based on the current checksum.
Add the retrieved digit to the current checksum.
Update the digit variable to the current digit.
Repeat this process for each digit in the reversed number.
Step 5: Calculate the check digit
After performing the calculations for all the digits, the check digit is the digit that, when added to the current checksum, will make the checksum a multiple of 10.
Find the digit from the D5 table that, when added to the current checksum, results in a multiple of 10. This digit is the check digit.
Step 6: Append the check digit
Append the check digit to the original number to obtain the final number with the appended check digit.
For the given number 45723, using the Verhoeff scheme, the check digit is calculated as follows:
Reversed number: 32754
Calculations:
For the first digit 4: Look up the digit in the D5 table at row 0, column 4. The retrieved digit is 3. Add 3 to the checksum. Update digit to 4.
For the second digit 5: Look up the digit in the D5 table at row 3 column 1. The retrieved digit is 4. Add 4 to the checksum. Update digit to 5.
For the third digit 7: Look up the digit in the D5 table at row 4, column 2. The retrieved digit is 1. Add 1 to the checksum. Update digit to 7.
For the fourth digit 2: Look up the digit in the D5 table at row 1, column 3. The retrieved digit is 1. Add 1 to the checksum. Update digit to 2.
For the fifth digit 3: Look up the digit in the D5 table at row 2, column 0. The retrieved digit is 2. Add 2 to the checksum. Update digit to 3.
The "checksum" after all calculations: 11
Finding the check digit:
We need to find a digit from the D5 table that, when added to the checksum of 11, results in a multiple of 10. From the table, we can see that adding digit 9 (row 1, column 4) to 11 gives us 20, which is a multiple of 10.
Therefore, the check digit for the number 45723
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