University of Illinois at Urbana Champaign Spring

University of Illinois at Urbana-Champaign Spring 2007 Math 181 Group F1 Quiz 8 Friday, April 20th. NAME 1. Remember that the check-digit for an ISBN number a1a2 . . . a10 is chosen in such a way that 10a1 + 9a2 + 8a3 + 7a4 + 6a5 + 5a6 + 4a7 + 3a8 + 2a9 + a10 is evenly divisible by 11. Is the number 0? 2435? 6411? 3 a correct ISBN number? Answer. The sum 10a1 +9a2 +8a3 +7a4 +6a5 +5a6 +4a7 +3a8 +2a9 +a10 is here equal to 10.0+9.2+8.4+ 7.3.+6.5+5.6+4.4+3.1+2.1+3 = 154, and 155 is not evenly divisible by 11. So the number 0?2435?6411?3 is not a correct ISBN number. 2. The check-digit a10 for a nine-digit ZIP+4 code a1a2 . . . a9 is chosen in such a way that a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10 ends with a 0. (a) Find the check-digit for the ZIP+4 code 55811? 2742. Answer. One has 5 + 5 + 8 + 1 + 1 + 2 + 7 + 4 + 2 = 35, so one must choose 5 as the check digit (b) Is the ZIP+4 code (including its check-digit) 5431275001 correct (explain)? If not, can you correct it? If you know

• transmission error


• a10 ends


• error unless


• code words


• digit


• urbana-champaign spring


• correct code


• only incorrect