Engaging math activities for the summer break - Day 17
Every book carries an ISBN or EAN-13 or both numbers. ISBN or EAN-13 are two ways to encode information that would allow to identify a book on the market. ISBN contains 10 digits EAN-13 thirteen. All but the last digit encode country, manufacturer (publisher), and product (book) information. The last digit serves as a safeguard from possible misprints. The two encodings differ in the manner they define the last digit.
What is the task? Pick several books and verify that their ISBN or EAN-13 encodings are correct. Learn to convert between the two. Practice addition and multiplication of small numbers and arithmetic modulo 10 and 11.
The ISBN encoding shows the country code (0 - USA), the manufactrurer (205 - Prentice Hall), the product id (02880) for that manufacturer, and the safety - 2. The corresponding EAN-13 number is displayed without the dashes, they are present in the complete specifications. Compared to ISBN, EAN-13 prepends 978 and changes the safety digit.
The safety calculations for ISBN The ten digits of an ISBN must satisfy the identity
10×d1 + 9×d2 + 8×d3 + ... + 1×d10 ≡ 0 (mod 11).
If, as the result of calculations, the last digit comes out to be 10, an 'X' is written instead.
Taking 0-205-02880-2 as example, we need to compute
10×0 + 9×2 + 8×0 + 7×5 + 6×0 + 5×2 + 4×8 + 3×8 + 2×0 = 109 ≡ -2 (mod 11)
which just confirms that the safety digit is 2.
The safety calculations for EAN-13
The thirteen digits in the EAN-13 encoding must satisfy
d1 + 3×d2 + d3 + 3×d4 + ... + d11 + 3×d12 + d13 = 0 (mod 10).
Turning again to the above example
9 + 3×7 + 8 + 3×0 + 2 + 3×0 + 5 + 3×0 + 2 + 3×8 + 8 + 3×0 = 79 ≡ -1 (mod 10),
implying that the safety digit has to be 1.
How to convert between ISBN and EAN-13? Discard the safety digit, either drop "978" or add it, and then recompute the safety digit as defined above.
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