Code_ The Hidden Language of Computer Hardware and Software - Charles Petzold [33]
0 51000 01251 7
This is very disappointing. As you can see, these are precisely the same numbers that are conveniently printed at the bottom of the UPC. (This makes a lot of sense because if the scanner can't read the code for some reason, the person at the register can manually enter the numbers. Indeed, you've undoubtedly seen this happen.) We didn't have to go through all that work to decode them, and moreover, we haven't come close to decoding any secret information. Yet there isn't anything left in the UPC to decode. Those 30 vertical lines resolve to just 12 digits.
The first digit (a 0 in this case) is known as the number system character. A 0 means that this is a regular UPC code. If the UPC appeared on variable-weight grocery items such as meat or produce, the code would be a 2. Coupons are coded with a 5.
The next five digits make up the manufacturer code. In this case, 51000 is the code for the Campbell Soup Company. All Campbell products have this code. The five digits that follow (01251) are the code for a particular product of that company, in this case, the code for a 10 ¾-ounce can of chicken noodle soup. This product code has meaning only when combined with the manufacturer's code. Another company's chicken noodle soup might have a different product code, and a product code of 01251 might mean something totally different from another manufacturer.
Contrary to popular belief, the UPC doesn't include the price of the item. That information has to be retrieved from the computer that the store uses in conjunction with the checkout scanners.
The final digit (a 7 in this case) is called the modulo check character. This character enables yet another form of error checking. To examine how this works, let's assign each of the first 11 digits (0 51000 01251 in our example) a letter:
A BCDEF GHIJK
Now calculate the following:
3 x (A + C + E + G + I + K) + (B + D + F + H + J)
and subtract that from the next highest multiple of 10. That's called the modulo check character. In the case of Campbell's Chicken Noodle Soup, we have
3 x (0 + 1 + 0 + 0 + 2 + 1) + (5 + 0 + 0 + 1 + 5) = 3 x 4 + 11 = 23
The next highest multiple of 10 is 30, so
30 – 23 = 7
and that's the modulo check character printed and encoded in the UPC. This is a form of redundancy. If the computer controlling the scanner doesn't calculate the same modulo check character as the one encoded in the UPC, the computer won't accept the UPC as valid.
Normally, only 4 bits would be required to specify a decimal digit from 0 through 9. The UPC uses 7 bits per digit. Overall, the UPC uses 95 bits to encode only 11 useful decimal digits. Actually, the UPC includes blank space (equivalent to nine 0 bits) at both the left and the right side of the guard pattern. That means the entire UPC requires 113 bits to encode 11 decimal digits, or over 10 bits per decimal digit!
Part of this overkill is necessary for error checking, as we've seen. A product code such as this wouldn't be very useful if it could be easily altered by a customer wielding a felt-tip pen.
The UPC also benefits by being readable in both directions. If the first digits that the scanning device decodes have even parity (that is, an even number of 1 bits in each 7-bit code), the scanner knows that it's interpreting the UPC code from right to left. The computer system then uses this table to decode the right-side digits:
Table 9-3. Right-Side Codes in Reverse
0100111 = 0
0111001 = 5
0110011 = 1
0000101 = 6
0011011 = 2
0010001 = 7
0100001 = 3
0001001 = 8
0011101 = 4
0010111 = 9
and this table for the left-side digits:
Table 9-4. Left-Side Codes in Reverse
1011000 = 0
1000110 = 5
1001100 = 1
1111010 = 6
1100100 = 2
1101110 = 7
1011110 = 3
1110110 = 8
1100010 = 4
1101000 = 9
These 7-bit codes are all different from the codes read when the UPC is scanned from left to right. There's no ambiguity.
We began looking at codes in this book with Morse code, composed of dots, dashes, and pauses between the dots and dashes. Morse code doesn't immediately