Assume that a movie is two hours long, that the frame rate is 30 frames per second, and that the resolution per frame is 1080i (1920x1090 pixels per frame), and that each pixel is represented by three colors (Red, Green, Blue) where each color is described by one byte.
A) how much storage is needed for the movie if there is no data compression?
B) Assuming that a movie can be stored on one DVD (4.7 GB), by what factor must the movie be compressed?
A) To calculate the storage needed for the movie without compression, we need to find the total number of frames and then multiply it by the size of each frame.
1. First, we need to calculate the number of frames in a two-hour movie. We know the frame rate is 30 frames per second (fps), so we can multiply the frame rate by the number of seconds in two hours (2 hours * 60 minutes * 60 seconds) to get the total number of frames:
Total Frames = 30 fps * (2 hours * 60 minutes * 60 seconds)
= 30 * 2 * 60 * 60 frames
= 216,000 frames
2. Next, we calculate the size of each frame by multiplying the resolution (1920x1080 pixels) by the number of bytes per pixel (3 bytes):
Size of Each Frame = 1920 pixels * 1080 pixels * 3 bytes
= 6,220,800 bytes
3. Finally, to find the total storage needed, we multiply the size of each frame by the total number of frames:
Total Storage = Size of Each Frame * Total Frames
= 6,220,800 bytes * 216,000 frames
ā 1,345,651,200,000 bytes
Therefore, without data compression, the movie would require approximately 1,345,651,200,000 bytes of storage.
B) To determine by what factor the movie must be compressed to fit on a DVD (4.7 GB), we need to compare the required storage without compression to the available storage on the DVD.
1. Convert the DVD storage from gigabytes to bytes:
DVD Storage = 4.7 GB * 1024 MB/GB * 1024 KB/MB * 1024 B/KB
= 4,700,000,000 bytes
2. Divide the required storage without compression by the available DVD storage:
Compression Factor = Total Storage / DVD Storage
= 1,345,651,200,000 bytes / 4,700,000,000 bytes
ā 286.27
Therefore, the movie must be compressed by a factor of approximately 286.27 to fit on one DVD.