If an image has only 4 colors, how many bits are necessary to represent one pixel’s color? Describe a new custom encoding that uses fewer bits to represent each color in the image. What is your encoding for each color? If you were to re-encode this image using your new encoding, how many bits would you save when compared to the 24 bit RGB encoding?

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Omer08

Answer:

1) 2 bits 2) shown in explanation 3) shown in explanation 4) 22 bits per pixel (2.75 bytes)

Explanation:

As a bit is one of two states, 1 or 0, 2 bits is sufficient to represent 4 colors:

00 = color 1

01 = color 2,

10 = color 3,

11 = color 4

This would be the custom type of encoding for that specific image as it only uses 4 colors.

Now to calculate the amount of memory saved, which is quite simple:

24-2=22

So you Would save 22 bits per pixel or 2.75 bytes per pixel.

RGB is a colour complementary wherein the main light colors of red, green, and blue are coupled in distinct ways of representing a range of colors. It uses to design is named again for preliminary colors red, blue and green of 3 primary additive color schemes.

Following are the solution to the given question:

  • Calculating the number of total bits which is required:

          [tex]\bold{= \log_2\ \text{(total number of colors)}}\\\\\bold{= \log_2\ (4)}\\\\\bold{= 2}[/tex]

  • Because only 4 colors seem to be prevalent, we could have the very next global color encoding:

             [tex]\to \bold{ Black = 00}\\\\\to \bold{White= 01}\\\\\to \bold{Red= 10}\\\\\to \bold{Blue= 11}\\[/tex]

  • So, the number of total bits through the image:

              [tex]\to \bold{= (17 \times 20) \times 24} \ \bold{= 8160}[/tex]  

          The number of total bits for the picture now is custom encoded                                  

            [tex]\to \bold{= (17 \times 20) \times 2} \ \bold{= 680}[/tex]

            Calculating the percentage:

               [tex]\bold{= \frac{\text{(original bits - new bits)} \times 100}{\text{original bits}}}\\\\\bold{= \frac{(8160 - 680) \times 100}{8160}}\\\\\bold{= \frac{7480 \times 100}{8160}}\\\\\bold{= \frac{748000}{8160}}\\\\\bold{= 91.67\%}[/tex]

So, the final answer is "2,00,01,10,11, and 91.67%"

Note:

Please find the complete question in the attached file.

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