This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.
GoalYou are given a line of 95 bits sequence scanline representing an image received from a barcode scanner.
The sequence is in EAN-13 format barcode.
NOTE The input sequence might be given in reversed order. This relates to a real life scenario when scanning the barcode upside-down.
Your mission is to decode this barcode into its decimal 13-digit representation.
Input binary sequence consist of the following blocks:
Guards allow the scanner to identify the start and end of the barcode in an image as well as the width of the bits.
LEFT PART and RIGHT PART each consist of 6 7-bit codes.
Left part may have digits coded with both L-code (which have odd parity) and G-code (even parity).
Right part consists of only even parity R-codes.
You may also notice that R-code is a reversed version of G-code and an inverted version of L-code.
Digit L-code G-code R-code
0 0001101 0100111 1110010
1 0011001 0110011 1100110
2 0010011 0011011 1101100
3 0111101 0100001 1000010
4 0100011 0011101 1011100
5 0110001 0111001 1001110
6 0101111 0000101 1010000
7 0111011 0010001 1000100
8 0110111 0001001 1001000
9 0001011 0010111 1110100
Please refer to https://imgur.com/3kKOkIX for a visual example.
So at this point you are able to reconstruct the last 12 digits.
The first EAN-13 digit is encoded by the pattern of L and G codes in LEFT PART using the table below.
First digit First group of 6 digits Last group of 6 digits
0 LLLLLL RRRRRR
1 LLGLGG RRRRRR
2 LLGGLG RRRRRR
3 LLGGGL RRRRRR
4 LGLLGG RRRRRR
5 LGGLLG RRRRRR
6 LGGGLL RRRRRR
7 LGLGLG RRRRRR
8 LGLGGL RRRRRR
9 LGGLGL RRRRRR
Finally, to verify a barcode after decoding, the following
Multiply every second digit by 3, then add up all the digits. If barcode is correct it's checksum would be a multiple of 10.
It's easier to understand an example of encoding rather than decoding.
Suppose we want to encode the number 4003994155486.
The first digit is 4, so we will use the pattern LGLLGG in the left part.
We then look up codes 0(L), 0(G), 3(L), 9(L), 9(G), 4(G) in the table:
0001101 0100111 0111101 0001011 0010111 0011101
For the right part we look up 1(R), 5(R), 5(R), 4(R), 8(R), 6(R) :
1100110 1001110 1001110 1011100 1001000 1010000
Finally, add the guards.
The first 3 digits of EAN-13 correspond to a country code. So, by reading barcodes printed on different products you may identify the country each product was manufactured in.
A string scanline of 95 bits representing a scanned EAN-13 barcode line of pixels (0-white, 1-black)
A single line of 13 decimal numbers without spaces representing decoded EAN-13 barcode or
INVALID SCAN in case any corruption of the input sequence detected.
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