A Introduction We learned about one dimensional analog to digital conversion in a previous lecture (Sample, Quantize, and En

A

Introduction

We learned about one dimensional analog to digital conversion in a previous lecture (Sample, Quantize, and Encode). We also learned that for capturing pictures, a CCD (or Charged Coupling Device) is the sensor to capture the light and convert to a 2D image by building the image in pixels, short for pixel elements. In this project, you will learn how a computer can represent an image with binary digits.

Encoding Bits

In class, we also mentioned each 0 or 1 is called a bit, and creating a sequence of 8 bits is called a byte. Information is stored in these 0’s and 1’s. In class, I gave the example of having a sequence of 2 bits. For two bits, there are only two positions and only four possible combinations of these zeros and ones (i.e., 00, 01, 10, 11). Now if I were to encode information to these particular sequences, this would only give me 4 possible options. I can, let’s say, choose the letter ‘A’ to be encoded by 00, ‘B’ to be encoded by 01, ‘C’ by 10, and ‘D’ by 11. But that’s it! So while I can technically encode these four options, it does not make any sense if I were to send a message to someone since I am missing the remainder of the alphabet! This means I will need to have more positions of these bits available to include all letters of the alphabet.

To encode more information, we will need more bits in a stream of data. For every position, N, we will have 2^N possible combinations of zeros and ones. For example, for a two bit sequence, I have that N = 2 and that I will have 2^N = 2² = 4 possible combination of zeros and ones.

Pixels

Pixels are two dimensional samples where each pixel is input as a binary stream of 0’s and 1’s for the computer to process and understand. Each pixel will represent a specific color as seen in a bitmap. When we have black and white images, we will only need 1 bit to represent each pixel of color. Here N = 1 and 2^N = 2¹ = 2 possible outcomes (either black or white).

For the computer to know this information, additional ‘metadata’ is needed. This metadata includes the color depth (the number of bits per pixel), and the resolution (the height times the width in pixels). 

Bitmap Storage

There is an associated file size for each image. In the aw form, no compression takes place and the file size will depend on the resolution and the color depth. The following equation can be used to calculate the file size. 

𝑆𝑖𝑧𝑒=𝑊𝑖𝑑𝑡ℎ𝑥𝐻𝑒𝑖𝑔ℎ𝑡𝑥𝐶𝑜𝑙𝑜𝑟𝐷𝑒𝑝𝑡ℎSize=WidthxHeightxColorDepth

The unit for this equation will be in bits. Typically, you will find units of storage size to be in bytes, where 1 byte is equal to 8 bits, so unit conversion will need to take place. Now, since file sizes can get really large, so instead of writing a very large file size in terms of bytes, it will be converted to be in units of kilobytes (kB), megabytes (MB), gigabytes (GB), or even terabytes (TB). Use the following prefix values:

For example, if I had a file size of 52,895,234 bits and I wanted to convert this into megabytes (MB), I would recall there are 8 bits in one byte and there are 1,048,576 bytes in one megabyte. These are my conversions. So, starting with the original value and multiplying with the ratios of the conversion equations:

52,895,234𝑏𝑖𝑡𝑠⋅1𝑏𝑦𝑡𝑒8𝑏𝑖𝑡𝑠⋅1𝑚𝑒𝑔𝑎𝑏𝑦𝑡𝑒1,048,576𝑏𝑦𝑡𝑒𝑠=6.3𝑀𝐵52,895,234bits⋅1byte8bits⋅1megabyte1,048,576bytes=6.3MB 

Notice the unit bits in the numerator cancels with bits in the denominator and bytes in the numerator cancels with bytes in the denominator and we are left with megabytes as the final unit.

RGB

When dealing with light, the three primary colors are red, green, and blue. The various colors of the rainbow are obtained from the combination of any of these colors. When using a device relying on light (TV screens, computer screens, etc.), one red, one green, and one blue comprise of a single pixel. When creating a digital color image, we use a 24 bit true color encoding. This means red, green, and blue are each assigned an 8 bit string for their particular contribution in the final color of a pixel. When the 8 bit string is 0000000 for either red, green, or blue, this means there is zero contribution of that color (RGB) to the pixel’s final color. When the 8 bit string is 11111111 for either red, green, or blue, this means there is complete contribution of that color and we assign the number 255 (this is the decimal equivalent of the binary string 11111111). We will see that any picture editor with a color palette will include values of 0 – 255 each for red, green, or blue colors for a total of 256 different states for each color.

Binary to Decimal Conversion

We went over binary placement and the decimal equivalent for the particular binary string in class. You can watch  to go over this again. This video is created for one of my other classes, but it contains all the information you need to help understand why does 00000000 equal 0, 11111111equal 255, or even why, for example, 00000110 equals 6.

Start the video from the beginning to gain an overview of different numbering systems. At the 1:18mark, I talk about the decimal system; at 3:51 I discuss the binary system; and at the 4:23 mark, I talk about converting from binary to decimal, and following that is the decimal to binary conversion.

****NEW***

You can also to help you.

Instructions

There will be two parts to this project. You will use Google Documents when submitting this project. Name the document with your Last Name, First Name Project 1. Include the title of the project at the top of the document and label each section accordingly. Adjust the sharing settings to make sure I am able to access the document. You will submit the URL of the document to Canvas when submitting this assignment.

Part 1: Using binary to create black and white images

With the following , you will create pixelated black and white images by using the notation of ‘0’ to represent a black square and a ‘1’ to represent a white square. Use the example of the flower in the editor to see how the image can be created. Simply copy and paste into the input box to see the flower example with the recommended resolution.

A) Create a checkerboard with a width of 8 pixels and a height of 8 pixels. Create a screenshot of your final work and place in the document under the label ‘Part 1.’ Find the total number of pixels for each image, and find the file size in units of bytes. 

B) Create a ladder with a width of 5 pixels and a height of 20 pixels. Create a screenshot of your final work and place in the document under the label ‘Part 1.’ Find the total number of pixels for each image, and find the file size in units of bytes. 

C) Freestyle it! Create a third image with a resolution of your choosing. You can play around with the height and the width resolution to find one that you are happy with. Be creative and, overall, have fun with this! Create a screenshot of your final work and place in the document under the label ‘Part 1.’ Find the total number of pixels for each image, and find the file size in units of bytes. 

D) Can you guess the image? You will be given a bit stream of data and will need to figure out what is this image. Start with height and width represented with 1 pixel x 1 pixel. 

Insert the following code into the pixel :

111111111111111100011110001110000011000001000000000

000000000000000000000000000000000000000000000000000

000000000010000000000001110000000000111110000000011

1111100000011111111100001111111111100111111

Change the width and the height until the entire image is seen and fills up the screen. What is this image? At what resolution is the image seen at? Find the total number of pixels for each image, and find the file size in units of bytes. Create a screenshot of the image and place in the document under the label ‘Part 1.’

Questions

In addition to the questions asked in the text above, include answers to the following questions in the Part 1 section of your Google Document.

• When creating the images, what are some observations you made about the image scale, image resolution, the number of pixels, and the pixel sizes? 
• Why did you choose the specific resolution for your image in Section C?
• For part D, when you were at the halfway mark from the full resolution of the image, did you see half the image? Why or why not?
• What would you expect for any of the images if you were to create the image in color? How would the color depth be affected? Would the resolution change for the same images?
• What would you expect if we were to create a video of the black and white images? How would the parameters change?
• If you were to set the number of bits to 3 (N = 3), how many possible combinations of bits can I have?

Part 2: In Living Color!

With the following , you will create pixelated color images but now with a different color depth, or the number of bits per pixel. Note that for the particular editing tool, the first 8 bits refer to the image height, the second 8 bits refer to the image width, and the remaining bits refer to the pixels. The latter will be dependent on what you set the value in the editing tool. 

Press ‘Enter’ to place each string on a separate line. You will find if you separate the various bits, it will be easier to see. 

A) Try the example in the editing tool by copying and pasting the binary string into the input field with the corresponding color depth of 3 bits per pixel. How many colors are created? What colors are created? What is the 3 bit string for each of the colors? What is the corresponding resolution?

[Hint: You will notice similarities in the bits for specific colors as observed in Part 1.]

Create a screenshot of your final work and place in the document under the label ‘Part 2.’ Find the total number of pixels for each image, and find the file size in units of bytes. 

B) With the same color depth and resolution as in Section A, change the positions of all the colors so they are in different locations. You should still end up with the same colors as before. Create a screenshot of your final work and place in the document under the label ‘Part 2.’ Find the total number of pixels for each image, and find the file size in units of bytes.

C) Create a 4 x 4 image with 12 bits per pixel of any color combination that you like! Create a screenshot of your final work and place in the document under the label ‘Part 2.’ Find the total number of pixels for each image, and find the file size in units of bytes. 

*** Change to Extra Credit***D) SSU has recently changed it’s logo and updated their color palettes. From , create another image using only the SSU-approved colors! You can choose any resolution, color depth, and scale as you like! Have fun and be creative! Find the total number of pixels for each image, and find the file size in units of bytes. 

Don’t forget that you will need to convert from decimal to binary to find the specific shades; refer to my video.

[Note: you will notice there are three ways of defining each color: CMYK (Cyan, Magenta, Yellow, Black), RGB (Red, Green, Blue), and HEX (short for hexadecimal). Please use the RGB values for this assignment.] 

Questions

In addition to the questions asked in the text above, include answers to the following questions in the Part 2 section of your Google Document.

• What are some observations you made with Part 2 as compared with Part 1?
• What do you observe for the total number of pixels and the file size in Section B as compared with Section A?
• For the 24 bit true color resolution where each color (RGB) can have 256 possible values, how many possible color combinations could I possibly have?