Calculating a check digit with weights and modulus 11
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. What is the first step when calculating a weighted check digit?
2. After multiplying each digit by its weight, what do you do with the products?
3. Digits 2, 5, 1 have weights 4, 3, 2. What is the weighted total?
4. A weighted total is 25. What is the remainder when it is divided by 11?
5. A scheme says the check digit is 11 minus the remainder. The remainder is 3. What is the check digit?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1total MOD 11 | AThe remainder was used directly as the check digit. This scheme needs 11 minus the remainder, so the check digit should be 11 - 9 = 2. | |
| 211 - (130 MOD 11) = 2 | BCheck digit 2 for the ISBN-10 digits 030640615 when the weighted total is 130 | |
| 3Multiply each digit by its weight and add the results: digits 5, 2, 1 with weights 4, 3, 2 | CA check digit must be a single character. In ISBN-10 a result of 10 is written as the letter X. | |
| 4Divide the total by 11, find the remainder, then take 11 minus the remainder to get the check digit | D5*4 + 2*3 + 1*2 = 28 | |
| 5Total = 130, 130 MOD 11 = 9, check digit = 9 | EThe remainder left after dividing the weighted total by 11 | |
| 611 - remainder = 10, so the ISBN-10 ends in 10 | F28 MOD 11 = 6, 11 - 6 = 5 |
C
Definitions
weighted check digit
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
remainder ← total MOD __
2.
check ← 11 - _________
3.
IF check = __ THEN
check ← "X"
ENDIF
4.
product ← digit _ weight
total ← total + product
5.
total ← total + product
remainder ← total ___ 11
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
d ← [5, 1, 7]
B
w ← [4, 3, 2]
C
total ← 5*4 + 1*3 + 7*2
D
rem ← total DIV 11
E
check ← 11 - rem
Question 2
A
total ← 37
B
rem ← total MOD 11
C
check ← 11 - rem
D
IF check = 11 THEN check ← "X"
Question 3
A
total ← 1
B
FOR i ← 1 TO 4
C
total ← total + d[i] * w[i]
D
NEXT i
Question 4
A
total ← 2*5 + 7*4 + 1*3
B
rem ← total MOD 11
C
check ← rem - 11
D
OUTPUT check
Question 5
A
total ← 0
B
FOR i ← 1 TO 9
C
total ← total + d[i] + w[i]
D
NEXT i
E
rem ← total MOD 11
Answer Key
Calculating a check digit with weights and modulus 11
Section A: Quick Questions
Q1
A — Multiply each digit by its weight
Q2
B — Add them up, then divide the total by 11 and find the remainder
Q3
B — 25
Q4
A — 3
Q5
A — 8
Section B: Match the Pairs
Q1
total MOD 11 → The remainder left after dividing the weighted total by 11
Q2
11 - (130 MOD 11) = 2 → Check digit 2 for the ISBN-10 digits 030640615 when the weighted total is 130
Q3
Multiply each digit by its weight and add the results: digits 5, 2, 1 with weights 4, 3, 2 → 5*4 + 2*3 + 1*2 = 28
Q4
Divide the total by 11, find the remainder, then take 11 minus the remainder to get the check digit → 28 MOD 11 = 6, 11 - 6 = 5
Q5
Total = 130, 130 MOD 11 = 9, check digit = 9 → The remainder was used directly as the check digit. This scheme needs 11 minus the remainder, so the check digit should be 11 - 9 = 2.
Q6
11 - remainder = 10, so the ISBN-10 ends in 10 → A check digit must be a single character. In ISBN-10 a result of 10 is written as the letter X.
Section C: Definitions
Q1
weighted check digit — Multiply each digit by its weight, add them up, divide by 11 and use the remainder (often 11 minus it) as the check digit. A 10 is written X in ISBN-10.Section D: Fill in the Blanks
Q1
remainder ← total MOD 11Q2
check ← 11 - remainderQ3
IF check = 10 THEN
check ← "X"
ENDIFQ4
product ← digit * weight
total ← total + productQ5
total ← total + product
remainder ← total MOD 11Section E: Spot the Error
Q1
D — DIV gives the whole-number quotient, but the check digit needs the remainder. It should be rem ← total MOD 11, which gives 37 MOD 11 = 4.
Q2
D — In ISBN-10 it is a check digit of 10 that is written as X, because 10 cannot fit in one digit. The test should be check = 10.
Q3
A — The running total must start at 0. Starting at 1 adds an extra amount to every sum, so the check digit comes out wrong. It should be total ← 0.
Q4
C — The scheme says the check digit is 11 minus the remainder, not the remainder minus 11, which would be negative. It should be check ← 11 - rem.
Q5
C — Each digit must be multiplied by its weight, not added to it. It should be total ← total + d[i] * w[i].