Maths and Computing:

The Key Stages related to Creating a QR Code

This is a step by step overview of the processes involved in creating a QR code containing a given series of characters.

• An encoding mode is chosen to determine how the characters will be encoded.
• Binary data can contain 7-bit ASCII characters or unicode characters that are encoded as multibyte characters using the UTF-8 encoding.
• Numeric data takes the least space, followed by alphanumeric and then binary
• If the data can be encoded in more that one way, then the one that takes the least space is chosen

• An error level determines the number of bytes that can be corrupted, detected and correntec.
• The four error levels are high, quartile, medium and low.
• The high error level requires the most space followed by quartile, medium and then low.
• The error level is determined accoring to whether it is more important to be able to correct data or to keep the size of the QR code low.

• With the input data, the encoding and the error level, the number of data bytes can be calculated..
• The number of data bytes determines the minimum QR code version that can be used..
• The QR Code grid can then be set up with the number of module based on the verison
• The static elements of the QR code are the positioning patterns, the timing patterns and the spacing. These can be added to the grid.

• There are eight different mask patterns.
• Any of these mask patterns can be applied to the data to create a valid QR code.
• Certain mask patterns create a better result with fewer blocks of white and black data.
• The result when each pattern is applied is rated, and the mask with the lowest ranking is chosen and applied to the data.

• The format information consists of fifteen bits.
• Two bits are used for the error level and three for the mask pattern. The rest are error correction bits.
• A mask is applied to the bits and the resulting bits are added to the QR code.
• The information bits are placed near to the two left positioning pattern
• A copy of the fifteen bits is also added to the QR code.

Terminology

Components of a QR Code

A QR code consists of a number of static elements that help determine the orientation and size of a QR code when it is being scanned.

The rest of the QR code is used to store the data relating to the information that is encoded within it.

• This QR code structure is for a version 1 QR code.
• The information in the QR code relates to Hello World with Binary encoding, Low error level and mask pattern 0.

Data Position in the QR Code

A version 1 QR code allows for 208 bits of data. This data is entered into the data area of the QR code

• The first bit is placed in the bottom right of the QR code.
• The last bit is placed on the far right just above the bottom left positioning pattern.
• The data goes up and down in a two module width columns, as shown below.
• If the data sequence reaches a point where it cannot continue, it jumps to the bottom right of the unused data space.

Table showing how data is positioned within the QR code

Data bits

The encoded data is then made up of:

1. The mode indicator for the encoding (4 bits)
2. The character count indicator block (The number of bits used depends on the encoding and the QR version)
3. The encoded data blocks
4. Padding data to complete any unused bytes.
5. Error Codes

QR Code Encoding

Encoding describes the method by which the characters are converted into bits of data that can be store in the QR code

• There are four standard encoding modes used by QR codes: numeric, alphanumeric, binary and kanji.
• All characters can be encoded using binary encoding although this may not be the most efficient selection.
• The selected encoding is stored as a 4-bit mode indicator at the beginning of the data.

Table of encoding types for a QR code

Numeric Encoding

Numeric encoding can be used if the data is made up entirely of the characters 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9

To encode the numeric characters:

• The digits are placed into groups of three from left to right to create values between 0 and 999.
• The 3-digit values are coverted to 10-bit binary numbers.
• If there is one remaining digit, it is multiplied by 16 and converted to an 8-bit binary number
• If there are two remaining digits, 2-digit value is multiplied by 2. The result is converted to an 8-bit binary number

Alphanumeric Encoding

Alphanumeric encoding can be used if the data is made up entirely of the following:

• Numeric digits
• Upper case letters
• Space
• The characters $ % * + - , / .

To encode the alphanumeric characters:

• Look up the value of each alphanumeric character.
• The values are taken in pairs.
• The first value of each pair is multiplied by 45 and added to the second value to form a value between 1 and 2024.
• This value is then converted to an 11-bit binary number.
• If there is one remaining character, its value is multiplied by 4 and converted to an 8-bit binary number.

Binary Encoding

Binary encoding can be used for any character that has a unicode value and is stored using one of more bytes using UTF-8 encoding.

For values between 0 and 127, one byte of data is used and the character is encoded using it's ASCII value.