Check Digit Scheme Based on D5

Verhoeff's Check digit scheme Catches all single digit errors Catches all transposition errors involving adjacent digits Uses only digits 0-9

Digital D5

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)

Check digit for 2935 Recall = (0 1 5 8 9 4 2 7)(3 6) Step 1: See page 112 for tables n 2935 –> 7*2*6*2*5(c) = 0 Now (7*2)*(6*2) = 5*9 = 1 So 5(c) = 1-1 = 4 Hence c = 0

Verify 29350 is legitimate 29450 is an error 29305 is an error