4-Color Run-Length Protocol Example
[rev. 11/5/2006]

Let us agree to the following file protocol:

1.	First 2 bytes are 4D 48 hex to indicate author’s initials (MH).
2.	Next 4 bytes are 46 4F 55 52 hex (the word FOUR) to indicate the type of protocol in use, namely Mr. Hansen’s 4-color compressed protocol.
3.	Next 2 bytes indicate height in pixels (stored little-endian).
4.	Next 2 bytes after that indicate width in pixels (stored little-endian).
5.	Next 3 bytes indicate the RGB color value to be represented by the 2-bit code 00. For example, if the color value is FF 00 FF (magenta), then each occurrence of 00 in the data will be interpreted as magenta.
6.	Next 3 bytes indicate the RGB color value associated with 01.
7.	Next 3 bytes indicate the RGB color value associated with 10.
8.	Next 3 bytes indicate the RGB color value associated with 11.
9.	Now that the header and color map are complete, the main data portion of the file can begin. Bitstream is to be interpreted as a group of 6-bit blocks, organized as follows: first 2 bits indicate the pixel color (00, 01, 10, or 11), and the next 4 bits indicate the repeat count. For example, consider the 12-bit sequence 9BC, which has 2 6-bit blocks, namely 100110 111100. The first group, 100110, indicates 2-bit color code “10” repeated 6 times, since 0110 is the binary representation of 6. The second group, 111100, indicates 2-bit color code “11” repeated 12 times, since 1100 is the binary representation of 12.
10.	Since data are in 6-bit blocks, it is possible that the last 6-bit block will not end on a byte boundary. If this occurs, the file will be padded with zeros to fill out the remaining byte evenly.
11.	The last byte of the file will be hex 1A (decimal 26) to indicate end of file.

The protocol above allows us to use any 4 colors we wish. However, for the Norwegian flag, we need the following color map:
   00 = white (same as RGB value FF FF FF hex)
   01 = blue (same as RGB value 00 00 FF hex)
   10 = red (same as RGB value FF 00 00 hex)
   11 = black (same as RGB value 00 00 00 hex)

Here is how the Norwegian flag bitmap would be encoded in hex as we implement the protocol above:

Step 1. 4D 48
Step 2. 46 4F 55 52
Step 3. 0C 00
Step 4. 24 00
Step 5. FF FF FF
Step 6. 00 00 FF
Step 7. FF 00 00
Step 8. 00 00 00

Step 9. *Note: Because each block is 6 bits, it takes 2 blocks to make 12 bits, which can be translated into 3 hex digits.

Action	Binary	Hex* (see note above)	Byte count
red repeated 5 times	10 0101		22 from above
white 1	00 0001	941	23.5
blue 2	01 0010
white 1	00 0001	481	25
red 14	10 1110
white 1	00 0001	B81	26.5
black 2	11 0010
white 2	00 0010	C82	28
black 1	11 0001
white 3	00 0011	C43	29.5
black 3	11 0011
white 1	00 0001	CC1	31
red 5	10 0101
white 1	00 0001	941	32.5
blue 2	01 0010
white 1	00 0001	481	34
red 14	10 1110
white 1	00 0001	B81	35.5
black 1	11 0001
white 1	00 0001	C41	37
black 1	11 0001
white 1	00 0001	C41	38.5
black 1	11 0001
white 2	00 0010	C42	40
black 1	11 0001
white 3	00 0011	C43	41.5
black 1	11 0001
red 5	10 0101	C65	43
white 1	00 0001
blue 2	01 0010	052	44.5
white 1	00 0001
red 14	10 1110	06E	46
white 1	00 0001
black 1	11 0001	071	47.5
white 2	00 0010
black 2	11 0010	0B2	49
white 3	00 0011
black 3	11 0011	0F3	50.5
white 1	00 0001
red 5	10 0101	065	52
white 1	00 0001
blue 2	01 0010	052	53.5
white 1	00 0001
red 14	10 1110	06E	55
white 15	00 1111
white 4	00 0100	3C4	56.5
blue 2	01 0010
white 15	00 1111	48F	58
white 2	00 0010
black 4	11 0100	0B4	59.5
white 2	00 0010
black 1	11 0001	0B1	61
white 3	00 0011
black 1	11 0001	0F1	62.5
blue 15	01 1111
blue 8	01 1000	7D8	64
white 2	00 0010
black 1	11 0001	0B1	65.5
white 3	00 0011
black 1	11 0001	0F1	67
white 1	00 0001
black 1	11 0001	071	68.5
white 1	00 0001
black 1	11 0001	071	70
white 1	00 0001
black 1	11 0001	071	71.5
blue 15	01 1111
blue 8	01 1000	7D8	73
white 2	00 0010
black 4	11 0100	0B4	74.5
white 2	00 0010
black 1	11 0001	0B1	76
white 1	00 0001
black 1	11 0001	071	77.5
white 1	00 0001
black 1	11 0001	071	79
white 6	00 0110
blue 2	01 0010	192	80.5
white 15	00 1111
white 2	00 0010	3C2	82
black 1	11 0001
white 2	00 0010	C42	83.5
black 2	11 0010
white 2	00 0010	C82	85
black 1	11 0001
white 1	00 0001	C41	86.5
black 1	11 0001
white 1	00 0001	C41	88
red 5	10 0101
white 1	00 0001	541	89.5
blue 2	01 0010
white 1	00 0001	481	91
red 14	10 1110
white 4	00 0100	B84	92.5
black 1	11 0001
white 8	00 1000	C48	94
red 5	10 0101
white 1	00 0001	941	95.5
blue 2	01 0010
white 1	00 0001	481	97
red 14	10 1110
white 3	00 0011	B83	98.5
black 1	11 0001
white 1	00 0001	C41	100
black 1	11 0001
white 2	00 0010	C42	101.5
black 1	11 0001
white 3	00 0011	C43	103
black 1	11 0001
red 5	10 0101	C65	104.5
white 1	00 0001
blue 2	01 0010	052	106
white 1	00 0001
red 14	10 1110	06E	107.5
white 2	00 0010
black 5	11 0101	0B5	109
white 2	00 0010
black 3	11 0011	0B3	110.5
white 1	00 0001
red 5	10 0101	065	112
white 1	00 0001
blue 2	01 0010	052	113.5
white 1	00 0001
red 14	10 1110	06E	115
white 2	00 0010
black 1	11 0001	0B1	116.5
white 3	00 0011
black 1	11 0001	0F1	118
white 3	00 0011
black 1	11 0001	0F1	119.5
white 2	00 0010	0 hex (rounds out the 120th byte), plus 2 leftover bits

10. Append 6 zero bits (000000) to finish out the 121st byte: 1000 0000 = 80 hex

11. Last byte: 1A

Here is the entire file, in hex:

4D 48 46 4F 55 52
0C 00 24 00
FF FF FF
00 00 FF
FF 00 00
00 00 00
94 14 81 B8 1C 82 C4 3C C1 94
14 81 B8 1C 41 C4 1C 42 C4 3C
65 05 20 6E 07 10 B2 0F 30 65
05 20 6E 3C 44 8F 0B 40 B1 0F
17 D8 0B 10 F1 07 10 71 07 17
D8 0B 40 B1 07 10 71 19 23 C2
C4 2C 82 C4 1C 41 54 14 81 B8
4C 48 94 14 81 B8 3C 41 C4 2C
43 C6 50 52 06 E0 B5 0B 30 65
05 20 6E 0B 10 F1 0F 10 80 1A

Total file size = 122 bytes = 976 bits.
If the bitmap had been stored as a raw (uncompressed) 2-bit-per-pixel map, the size required would have been 108 bytes (864 bits). Therefore, the run-length encoding scheme here did not save any storage space—in fact, it wasted space. However, this was largely because of the overhead consumed by the file header and color map. The “guts” of the file were only 99 bytes, which represents a modest savings.

With a cleverer compression protocol, it would be possible to save much more space. For example, since the rows of the flag consist of only 3 different patterns, the rows could be tokenized. The letters on the right side of the flag are monochrome and hence could be efficiently encoded as an uncompressed monochrome bitmap.