Final answer:
The information content of a four-megapixel image where each pixel can be one of 1024 colors is about 4.77 megabytes. This is calculated by multiplying the number of pixels (4 million) by the color bit depth (10 bits per pixel) and then converting the result from bits to megabytes.
Step-by-step explanation:
To calculate the information content of a picture displayed on a four-megapixel computer screen where each pixel can display one of 1024 colors, we need to understand two concepts: megapixels and color depth.
A megapixel represents one million pixels. A four-megapixel display has 4,000,000 pixels. The color depth here is 1024 possible colors for each pixel, which is equivalent to 10 bits of data per pixel since 210 = 1024.
To find the information content, we multiply the total number of pixels by the number of bits required to represent each pixel's color:
- Total pixels = 4,000,000
- Bits per pixel = 10
- Information content = Total pixels × Bits per pixel
- Information content = 4,000,000 × 10 bits
- Information content = 40,000,000 bits
Since there are 8 bits in one byte, we divide by 8 to convert the information content to bytes:
- Information content = 40,000,000 bits / 8
- Information content = 5,000,000 bytes
To convert bytes to megabytes, we divide by 1,048,576 (the number of bytes in a megabyte):
- Information content = 5,000,000 bytes / 1,048,576
- Information content ≈ 4.77 megabytes
The information content of the picture is approximately 4.77 megabytes. Note that this calculation does not take into account any file format overhead or compression that might be used to store the image.