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MatheMUSEments
Decoding Bar Codes
By Ivars Peterson
Muse, November 2001, p. 33.
Just about every package you buy at the supermarket
has a small label made of wide and narrow bars. This
pattern stands for a 12-digit number, called a Universal
Product Code (UPC), that identifies the product.
A 15-ounce box of Cheerios, for example, has the
following number:
0 16000 66610 8
The first digit, 0, gives the product category—in
this case, general groceries. The next five digits
(16000) identify the manufacturer (General Mills). The
following five digits (66610) identify the specific
product: a 15-ounce box of Cheerios. A larger or smaller
box would have a different number.
When you check out, the bar code is scanned and
the store’s computer retrieves the price for that
product. The computer also does some arithmetic to help
make sure the bar code scanned correctly. That’s where
the final digit of a UPC comes in. It’s called a check digit.
In the tiny amount of time before the price appears on a
cash register screen, the computer performs the following
calculation using the first 11 digits of the UPC.
- Adds the six digits in the odd positions: 0 + 6 + 0 + 6 + 6 + 0 = 18
- Multiplies the result by 3: 18 x 3 = 54
- Adds the five digits in the even positions: 54 + 1 + 0 + 0 + 6 + 1 = 62
- Subtracts the sum from the next-highest multiple of 10: 70 – 62 = 8
If the result matches the UPC check digit, as it does
in this case, the computer sends the price to the cash
register. If it doesn’t, the cashier hears a beep.
Try the calculation yourself on the UPC of your favorite
product. It’s amazing how much math goes on behind the
scenes-even at a grocery store!
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