Run Length Encoding: 20W, 8W5K7W, 9W3K8W, 7W7R6W, 6W4R1Y4R5W

[Villiers]

Homework Statement

The file size of this image is calculated by firstly determining the resolution or how many pixels there are: 20 x 20 = 400 pixels.

Each pixel is described by 8 bits so the file size is: 400 pixels x 8 bits = 3,200 bits or 400 bytes.

a) Run length encoding is applied to the file in order to reduce its file size. An encoded sequence of the same data is stored as 2 bytes: the value of the repetition and the colour code. For example the first line would be stored as 20W (the W would be the binary code for white but is summarised here as a character).

For each line show how the data would be encoded using the format: [LengthColour]. The first and fourth lines have been done for you.

(W=White, K=Black, R=Red, Y=Yellow, B=Blue, N=Brown)

Relevant Equations

b) Determine what the RLE compressed file size is bytes

Line Run length encoded sequence
1 20W
2 20W
3 20W
4 8W5K7W
5 8W5K7W
6 8W5K7W
7 8W5K7W
8 9W3K8W
9 7W7R6W
10 6W4R1Y4R5W
11 6W1R1W5R1W1R5W
12 6W1R1W2R1Y2R1W1R5W
13 6W1R1W5R1W1R5W
14 6W1R1W2R1Y2R1W1R5W
15 9W3B8W
16 9W3B8W
17 9W3B8W
18 9W3B8W
19 9W3B8W
20 8W5N7Wthe answer is 152 bytes but i don't understand how they arrived at this number.
any help would be appreciated.

 

[Baluncore]

Welcome to PF.

Count the bytes used to represent the number of pixels and the colour.

We do not have your original 400 byte data file. Please attach it to a post.
Obviously, we could regenerate it from the RLL data file.
But that would not check the algorithm employed if there was an error in the output file you present.

The first three lines are each 20 White pixels, = 2 bytes per line.
The count of 20 fits in the first byte, the W in the second byte.

The fourth line is 8 White, followed by 5 blacK, then 7 White pixels, = 6 bytes.
Notice that the numbers in any line should add up to 20.

 

[Villiers]

Hi

Thanks for your reply. I have the answer... i just don't understand the result and how it was derived. I have attached the answer document.
Would appreciate any advice :)https://docs.google.com/document/d/11gg55ZDuIsTfv9GJ1ivcv6VqxueO0YU7GBEyFxZ5XnA/edit?usp=sharing

 

[pbuk]

Would appreciate any advice

What part of the advice that has already been given do you need more help with?

 

[Villiers]

Hi
I know the answer is 152 bytes
but I don't understand how you get to this number.
i understand how each line has been compressed with 2 bytes per instance of a colour and that each line adds up to 20.
here is the original image file:
https://docs.google.com/document/d/11gg55ZDuIsTfv9GJ1ivcv6VqxueO0YU7GBEyFxZ5XnA/edit?usp=sharing

thanks

 

[Office_Shredder]

Can you write down how many bytes each line takes? Then add them up and see what you get.

 

[Villiers]

I get 156
Line Run length encoded sequence
1 20W 2 bytes
2 20W 2 bytes
3 20W 2 bytes
4 8W5K7W 6 bytes
5 8W5K7W 6 bytes
6 8W5K7W 6 bytes
7 8W5K7W 6 bytes
8 9W3K8W 6 bytes
9 7W7R6W 6 bytes
10 6W4R1Y4R5W 10 bytes
11 6W1R1W5R1W1R5W 14 bytes
12 6W1R1W2R1Y2R1W1R5W 18 bytes
13 6W1R1W5R1W1R5W 14 bytes
14 6W1R1W2R1Y2R1W1R5W 18 bytes
15 9W3B8W 6 bytes
16 9W3B8W 6 bytes
17 9W3B8W 6 bytes
18 9W3B8W 6 bytes
19 9W3B8W 6 bytes
20 8W5N7W 6 bytes

 

[Baluncore]

I get 156

2+2+2 + 6+6+6+6+6+6 + 10+14+18+14+18 + 6+6+6+6+6+6 = 152
Check your arithmetic, I get 152.

 

[Villiers]

thank you!