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July-August 2005  

thinking man
logo puzzle of the month 1 Puzzle #102
Quiz/test #12 logo pzm 2
logo pzm 3 W-kammer #12
   Enjoy solving Archimedes' Lab™ Puzzles!

triangle-square-circle Puzzle #102  
  Copy this page and cut out the largest possible square piece of Gruyère cheese without any hole... Not so obvious!
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solution puzzle 102
©2005 Archimedes' Lab

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circle-triangle Quiz #12 TOP
Verbal & Math Questions
Find a 5-digit number that, if we place a 9 at the beginning to make a new number, is 4 times larger than if we place the 9 at the end instead! How many common words end with -gry in English? Replace the question marks (?) with maths symbols (+-:x) and make the equation correct...

Wunderkammer #12 TOP

Every product has its fingerprint!

"If it exists, bar code it"
- Unknown author

  On October 20, 1949, N. J. Woodland and B. Silver filed a patent application titled "Classifying Apparatus and Method". The inventors described their invention as relating "to the art of article classification [...] through the medium of identifying patterns". The barcode is born... Barcodes, of course, are those ever-familiar 'bars' and 'numbers' on virtually everything.
  Barcodes represent numbers as a series of vertical lines. Each of the lines is either black or white, and the sequence of lines forms a pattern which is recognized as a particular digit when scanned by a computer. A single barcode digit represents actually 7 units or bits. For instance, the digit '1' is composed of the seven units, '0011001' or "space-space-bar-bar-space-space-bar". Every product is assigned a unique 12 or 13-digit number.
  On a UPC barcode the same digits on the left-hand side (Manufacturer Code) is coded differently than the digits on the right-hand side (Product Code). The left side digits are actually the 'inverted' or 'complementary' codes of the right side digits. The right-side codes are called even parity codes because there is an even number of 'black bar' units. The left-side is called odd-parity because there is an odd number of 'black bar' units. Having different coded numbers for each side allows the barcode to be scanned in either direction.

  The following table features the left and right side codes matching the corresponding digits, separated into seven single units or bits.

Left side (odd parity) codes
1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7
0 1 2 3 4
0001101 0011001 0010011 0111101 0100011
1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7
5 6 7 8 9
0110001 0101111 0111011 0110111 0001011
Right side (even parity) codes
1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7
0 1 2 3 4
1110011 1100110 1101100 1000010 1011100
1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7
5 6 7 8 9
1001110 1010000 1000100 1001000 1110100

Anatomy of a bar code

  Guard Bars are located at the beginning, middle and end of the barcode. The guard bars indicate the computer-scanner when the manufacturer and product code begin and end. The 3 guard bars are also the supposedly "666" (Number of the Beast!) hidden in the barcode. But is the number 666 truthfully hidden in the UPC barcode? Technically, no it isn't. The digit 6 and the three guard bars 'appear' to be identical, but they are different: the beginning and ending guard bars are encoded as '101'; and the middle guard bar, as '01010'. The digit 6 is a 7-unit code '1010000'. The beginning and ending guard bars are only three units, and middle guard bar is only five units. So, from a computer's perspective the number "666" is NOT in the UPC barcode!
  Check digit: Also called the 'self-check' digit. The check digit is on the outside right of the barcode. The check digit is an "old-programmer's trick" to validate the other digits (manufacturer and product code) were read correctly.
How the computer calculates the check digit
Below is the mathematical formula to calculate the check digit:
check digit formula
In other words, suppose you want to find the check digit of UPC barcode number 7-26412-17542.
Step 1: From the right to the left, start with odd position, assign the odd/even position to each digit: 7-26412-17542 (odd positions are in red).
Step 2: Sum all digits in odd position and multiply the result by 3. (7+6+1+1+5+2) x 3=66
Step 3: Sum all digits in even position. (2+4+2+7+4)=19
Step 4: Sum the results of step three and four: 66+19=85
Step 5: Divide the result of step four by 10. The check digit is the number which adds the remainder to 10. In our case, divide 85 by 10 we get the remainder 5. The check digit then is the result of 10-5=5.

More barcodes
There are many different types of barcodes. Each uses a series of varying width bars and spaces to encode numbers and/or letters and/or special characters. Some barcode symbologies were designed to encode only numbers while others can encode numbers. letters and even special computer control characters.

International Standard Book Number includes the price of the book in the bar code. The last 5 digits in this example translate to $44.95 US dollars.
Data Matrix
Two-dimensional bar code which can store 2,000 ASCII characters. It can encode a lot of information, in a small space, and adjust to be square or rectangular.

External links
small square Barcode art
small square Barcode generator

Related Books
Getting started with barcodes
by Bushnell.

getting started
The Barcode Implementation Guide
by Stephen Pearce.

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