Encoding the ZIP

• The USPS bar code is defined by the following:
  • Bits are represented as long (``1'') and short (``0'') vertical dashes.
  • The code aims to represent the digits 0, 1, $\ldots$, 9.
  • Each digit is represented by 5 bits (dashes).
  • Each code word of 5 bits contains exactly 2 long dashes.
    

    digit	binay code	bar code
    1	00011	| | | | |
    2	00101	| | | | |
    3	00110	| | | | |
    4	01001	| | | | |
    5	01010	| | | | |
    6	01100	| | | | |
    7	10001	| | | | |
    8	10010	| | | | |
    9	10100	| | | | |
    0	11000	| | | | |

  • A long dash is added on either side of the bar code.
  • An additional digit is appended. This digit is computed by:
    • adding all digits in the ZIP code,
    • determining the difference to next largest multiple of 10.
  • Example: The bar code below encodes: 22030 4444 00 7.
  • The last digit is 7, because 2+2+0+3+0+4+4+4+4+0+0+7=30.

  

Figure 2.18: USPS bar code for 22030-4444-00. The check digit is 7.