Question

Suppose an image is represented on a display screen by a square array containing 256 columns and 256 rows of pixels. If for each pixel, 3 bytes are required to encode the color and 8 bits to encode the intensity, how many bytesize memory cells are required to hold the entire picture?

Short answer

262144 bytes.

Step-by-step solution

Determine Total Number of Pixels

The image is represented by a square array with 256 columns and 256 rows. To find the total number of pixels, multiply the number of columns by the number of rows. Hence, the total number of pixels is:\[256 \times 256 = 65536 \text{ pixels}\]

Calculate Memory for Color Encoding

Each pixel requires 3 bytes to encode its color. Therefore, for all 65536 pixels, the total memory required for color encoding is calculated as:\[65536 \text{ pixels} \times 3 \text{ bytes/pixel} = 196608 \text{ bytes}\]

Calculate Memory for Intensity Encoding

Each pixel requires 8 bits to encode the intensity. Since there are 8 bits in a byte, each pixel requires 1 byte for intensity encoding. Thus, for 65536 pixels, the total memory required for intensity encoding is:\[65536 \text{ pixels} \times 1 \text{ byte/pixel} = 65536 \text{ bytes}\]

Compute Total Memory Required

Add the memory required for color encoding and intensity encoding to get the total memory needed to store the entire picture. Therefore:\[196608 \text{ bytes} + 65536 \text{ bytes} = 262144 \text{ bytes}\]

Conclusion

The total number of bytesize memory cells required to hold the entire picture is 262144 bytes.

Key concepts

Pixel Representation

Pixels are the smallest units of a digital image and form the basis of pixel representation. In a digital image, each pixel corresponds to a point in the image. In this example, the image is structured as a grid with 256 rows and 256 columns, leading to a matrix of individual pixels. Hence, the total number of pixels can be calculated by multiplying the number of rows by the number of columns:

\(256 \times 256 = 65536\) pixels. This multiplication gives us the total quantity of pixels in the entire image. Understanding pixel representation is crucial in digital imaging as it determines the resolution and thus the sharpness and detail visible in the image.

• 256 columns
• 256 rows
• Total pixels = 65536

Each pixel acts as a tiny dot that collectively creates the overall image we see.

Memory Calculation

Memory calculation is essential for understanding how much storage an image will require. Each pixel in our example is responsible for representing color and intensity.

By calculating the memory needed for these encodings, we ascertain the total memory needs for storing the entire image.

To determine the memory required, consider the needs for each pixel. Sum the memory used for parameters like color and intensity.

• Color requires 3 bytes to be represented for each pixel.
• Intensity requires 8 bits (which is equivalent to 1 byte) for each pixel.

To find the total storage means adding memory used for all pixels in each parameter.

Thus, by computing both for color encoding and intensity, you can get a comprehensive view of the image's storage requirements.

Color Encoding

Color encoding determines how color information is stored for each pixel. In our scenario, each pixel requires 3 bytes for this purpose. These 3 bytes typically reflect the RGB color model, assigning one byte each for red, green, and blue channels. Thus, a wide variety of colors can be represented by different combinations of these three channels.

For 65536 pixels:

• Total bytes for color = 65536 pixels \(\times\) 3 bytes/pixel = 196608 bytes

This means, a significant amount of memory is used just to store the color details for an entire image. Color encoding is essential in ensuring images maintain visual appeal and accuracy in representation.

Intensity Encoding

Intensity encoding in digital images signifies how light or dark a pixel appears based on its intensity value. Here, each pixel uses 8 bits (or 1 byte) for intensity encoding. This 8-bit range allows for the capture of 256 different intensity levels from very dark to very bright.

Calculating memory for all pixels' intensity gives:

• Total bytes for intensity = 65536 pixels \(\times\) 1 byte/pixel = 65536 bytes

By representing intensity this way, finer nuances in shading and brightness can be captured, contributing to the overall detail and quality of the image. Intensity encoding is crucial for ensuring that subtleties in texture and dimension are perceived correctly in any digital image.