0. Analyze Unicode characters

Number of code points in the input text string:

Details of each character:

Can every character be encoded in:

Chosen segment mode to encode all characters:

1. Create data segment

Convert each character to bits. For numeric and alphanumeric modes, consecutive characters are grouped together before being encoded into bits. For byte mode, a character produces either 8, 16, 24, or 32 bits.

The created single segment:

• Mode:
• Count:
• Data:

(This demo program always creates a single segment for simplicity. But it is possible to segment the text optimally to minimize the total bit length.)

2. Fit to version number

Total bit length needed to represent the list of segments, depending on version:

(Note: A codeword is defined as 8 bits, also known as a byte.)

QR Code capacity of data codewords per version and error correction level, and whether the data fits (green/red background):

Chosen version number:

3. Concatenate segments, add padding, make codewords

Join a variety of bit strings together:

Notes:

• The segment mode is always a 4-bit field.

• The character count’s field width depends on the mode and version.

• The terminator is normally four “0” bits, but fewer if the data codeword capacity is reached.

• The bit padding is between zero to seven “0” bits, to fill all unused bits in the last byte.

• The byte padding consists of alternating (hexadecimal) EC and 11 until the capacity is reached.

The entire sequence of data bits:

The entire sequence of data codeword bytes (by splitting the bit string into groups of 8 bits), displayed in hexadecimal:

4. Split blocks, add ECC, interleave

Statistics about all blocks:

Split the sequence of data codewords (green background) into short and long blocks; then for each block, compute the ECC codewords (blue) and append them to the end of the block:

(Note: The math behind computing the Reed–Solomon error correction codes is omitted because it is long, tedious, and not very interesting.)

The final sequence of codewords formed by interleaving data/ECC codewords from different blocks:

The final sequence of bits to draw in the zigzag scan:

5. Draw fixed patterns

Draw the horizontal and vertical timing patterns (on both row 6 and column 6, counting from 0 starting at the top left corner):

Draw finder patterns on the three corners, each of which is 8×8 including the separator, overwriting some timing modules:

Draw temporary dummy format bits (adjacent to the finders):

6. Draw codewords and remainder

Compute the zigzag scan (which starts from the bottom right corner) to visit all unfilled modules (i.e. skipping function modules):

Draw data/ECC modules according to the zigzag scan order and bit values from the final sequence of codewords:

(For example, the codeword byte C5 (hex) is 11000101 in binary, and produces the sequence of modules [dark, dark, light, light, light, dark, light, dark].)

7. Try applying each mask

Show: Mask pattern 0 Mask pattern 1 Mask pattern 2 Mask pattern 3 Mask pattern 4 Mask pattern 5 Mask pattern 6 Mask pattern 7

The mask pattern (only affects non-function modules):

XOR the mask to the modules of data, ECC, and remainder:

Draw the actual format bits (adjacent to the finders):

8. Find penalty patterns

Horizontal runs of same color modules (each at least 5 long):

Vertical runs of same color modules (each at least 5 long):

2×2 boxes of same color modules:

Horizontal finder-like patterns:

Vertical finder-like patterns:

Balance of dark/light modules:

9. Calculate penalty points, select best mask

Lowest total penalty points: Mask pattern

How penalties are calculated:

• RunP: 3 points for each 5-module linear run of the same color, 4 points for each 6-module run, 5 points for each 7-module run, 6 points for each 8-module run, etc. Runs cannot overlap.

• BoxP: 3 points for each 2×2 box of the same color. Boxes can overlap.

• FindP: 40 points for each finder-like pattern. Finder patterns can overlap.

• BalP: 0 points if the proportion of dark modules is in the range [45%, 55%]; 10 points if within [40%, 60%]; 20 points if within [35%, 65%]; 30 points if within [30%, 70%]; etc.