Check Digit Scheme

1
Check Digit Scheme

• Based on D5

2
Verhoeff's Check digit scheme

• Catches all single digit errors
• Catches all transposition errors involving
  adjacent digits
• Uses only digits 0-9

3
Digital D5
4
How it works

• Let?? (0 1 5 8 9 4 2 7)(3 6)
• ? is a permutation in S10
• The check digit for 2935 is c, where
• ?(2) ?2( 9) ?3(3) ?4(5) ?5(c) 0
• (multiplication is in digital D5)

5
Check digit for 2935

• Recall?? (0 1 5 8 9 4 2 7)(3 6)
• Step 1 See page 112 for tables ?n 2935 gt
  7262?5(c) 0
• Now (72)(62) 59 1
• So ?5(c) 1-1 4
• Hence c 0

6
Verify

• 29350 is legitimate
• 29450 is an error
• 29305 is an error