A hand-held video player displays 320*240 picture element (pixels) in each frame of the video. ?

Question

A hand-held video player displays 320*240 picture element (pixels) in each frame of the video. Each pixel requires 2 bytes of memory. Videos are displayed at a rate of 30 seconds per second. How many minutes of video will fit 30 gigabyte memory?

show me how to get the answer

Answer 1

1. Using the information about how many pixels, determine the simple number of pixels in each frame.

2. Using the information about how many bytes each pixel uses, etermine how many bytes those pixels require.

3. Using the number of bytes per frame and the number of frames per second, determine how many bytes are required for one second of video.

4. Using the bytes per second, find the number of bytes per minute of video.

5. Convert the total memory from its given measure to bytes.

6. Divide the total memory available by the bytes per minute of video to get the total number of minutes fit the available memory.

320 * 240 pixels/frame = 76,800 pixels/frame

76,800 pixels/frame * 2 bytes/pixel = 153,600 bytes/frame

153,600 bytes/frame * 30 frames/second = 4,608,000 bytes/second

4,608,000 bytes/second * 60 seconds/minute = 276,480,000 bytes/minute

30 gigabytes * 1,024 megabytes/gigabyte * 1,024 kilobytes/megabyte * 1,024 bytes/kilobyte = 32,212,254,720 bytes

32,212,254,720 bytes / {276,480,000 bytes/minute} = 116.5084444 minutes

So 116.5084444 minutes will fit. Let's round that to 116 minutes (one usually uses "4/5" rounding or reduces the answer to "significant digits" but since this is a real-world problem, I'll say rounding to 117 minutes (4/5) would be bad when someone counting on all of them finds himself cut off at 116.5 or so and that 100 or 120 minutes (significant digits) is too imprecise in a big way (100) and might cause the same problem 117 would (120). So let's go with 116 minutes and let the user be happily surprised, maybe.

One note:  given that it is a real material, sort of, based problem, one cannot use the common meaning of "gigabyte" as 1,000^3 rather than 1,024^3 without first making sure the 30 Gb value is indeed manufacturer puffery. Since it likely is, I give now the result assuming that 30 Gb = 30,000,000,000 bytes:  108.5069444 minutes, or 108 minutes using the above rounding reasoning.

For a math homework problem, 116 minutes is what I'd give. For a computer class problem, I'd deal in the reality of manufacturer puffery:  108 minutes. Ask about the rounding and significant digits policy of the teacher.