using this A video camera producing full screen 1920 × 1080 pixel true‐color images at a frame rate of thirty frames per second, for example, will generate 1920 pixels × 1080 pixels × 3 bytes of color/image × 30 frames per second = 178 MB of data per second! A one‐minute film clip would consume 10.4 GB of storage... how can we figure out ths=is?  If true color requires 3 bytes per pixel, how much storage space is required for a  minute's worth of output for a video camera producing full screen 1024 × 768 pixel true color images at a frame rate of thirty frames per second? Explain any assumptions you  make about your calculations. 

To calculate the storage space required for a one-minute video clip, let's break down the problem and perform the calculations step by step. 

### Step 1: Determine the total number of pixels per frame
The video resolution is given as 1024 × 768 pixels.

\[
\text{Total pixels per frame} = 1024 \times 768 = 786,432 \text{ pixels}
\]

### Step 2: Determine the number of bytes per pixel
Each pixel requires 3 bytes to represent true color.

\[
\text{Bytes per pixel} = 3 \text{ bytes}
\]

### Step 3: Calculate the total number of bytes per frame
Now, multiply the total number of pixels by the bytes per pixel to find the total number of bytes per frame.

\[
\text{Bytes per frame} = 786,432 \text{ pixels} \times 3 \text{ bytes/pixel} = 2,359,296 \text{ bytes/frame}
\]

### Step 4: Calculate the number of bytes per second
The video camera captures 30 frames per second, so multiply the bytes per frame by the number of frames per second.

\[
\text{Bytes per second} = 2,359,296 \text{ bytes/frame} \times 30 \text{ frames/second} = 70,778,880 \text{ bytes/second}
\]

### Step 5: Convert bytes per second to megabytes per second
There are 1,048,576 bytes in a megabyte (MB).

\[
\text{MB per second} = \frac{70,778,880 \text{ bytes/second}}{1,048,576 \text{ bytes/MB}} \approx 67.5 \text{ MB/second}
\]

### Step 6: Calculate the storage space required for a one-minute video
Since there are 60 seconds in a minute, multiply the MB per second by 60.

\[
\text{Storage space for 1 minute} = 67.5 \text{ MB/second} \times 60 \text{ seconds} = 4,050 \text{ MB}
\]

### Final Answer
The storage space required for a one-minute video clip is **approximately 4,050 MB** or **4.05 GB**.

### Assumptions:
1. **No compression:** The calculation assumes that the video is uncompressed.
2. **Consistent frame rate and resolution:** The frame rate (30 fps) and resolution (1024 × 768 pixels) are consistent throughout the video.
3. **True color:** Each pixel requires exactly 3 bytes (24 bits) for true color representation.

Would you like any further details or have any questions?

### Relative Questions
1. How would the storage requirement change if the frame rate was 60 fps instead of 30 fps?
2. What is the effect of video compression on the required storage space?
3. How does increasing the resolution from 1024 × 768 to 1920 × 1080 pixels impact storage requirements?
4. What would be the storage space needed for a 10-minute video at the same resolution and frame rate?
5. How would the storage space required compare between a grayscale video and a true color video?

### Tip:
When dealing with large video files, it's important to consider using video compression techniques to significantly reduce storage requirements without losing noticeable quality.

A video camera producing full screen 1024 × 768 pixel true-color images at a frame rate of thirty frames per second, for example, will generate how much storage space for a one-minute video? True color requires 3 bytes per pixel. Explain any assumptions you make about your calculations.

Learn how to calculate the storage space needed for a one-minute video clip at 1024 × 768 resolution and 30 frames per second in true color. This step-by-step guide uses key formulas to help students understand data storage calculations, assuming no compression and constant resolution. Suitable for Grades 9-12.

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