A 512×512512×512 raw grayscale image with each pixel value ranging from 0 to 255 requires approximately _____ kb of memory storage.

1. Break Down the Problem

To find the memory storage required for the image, we need to consider:

• The dimensions of the image (512 × 512).
• The pixel value range (0 to 255), which determines the bits required to represent each pixel.

2. Relevant Concepts

1. Number of pixels: Calculate the total number of pixels in the image.
2. Bits per pixel: Since the pixel values range from 0 to 255, each pixel can be represented using 8 bits (as $2^8 = 256$).
3. Total memory: Multiply the total number of pixels by bits per pixel, and then convert bits to kilobytes.

3. Analysis and Detail

1. Calculate the total number of pixels: $\text{Total pixels} = 512 \times 512 = 262144$

2. Calculate the total bits required: $\text{Total bits} = \text{Total pixels} \times 8 = 262144 \times 8 = 2097152 \text{ bits}$

3. Convert bits to bytes: $\text{Total bytes} = \frac{2097152}{8} = 262144 \text{ bytes}$

4. Convert bytes to kilobytes: $\text{Total kilobytes} = \frac{262144}{1024} = 256 \text{ KB}$

4. Verify and Summarize

The calculations confirm that the image requires 256 KB of memory storage when considering all pixels and the bits needed to represent their values.

Final Answer

The memory storage required is approximately 256 KB.