Question

It is desired to send a sequence of computer screen images over an optical fiber. The screen is \(3840 \times 2160\) pixels, each pixel being 24 bits. There are 50 screen images per second. What data rate is needed is needed?

Short answer

The data rate needed is 9,953,280,000 bits per second.

Step-by-step solution

Calculate Total Pixels per Image

First, find the number of pixels in one screen image. This is calculated by multiplying the width and height of the screen.\[ 3840 \times 2160 = 8,294,400 \text{ pixels} \]

Calculate Bits per Image

Next, determine how many bits are used per image. Each pixel requires 24 bits, so multiply the total number of pixels by 24.\[ 8,294,400 \times 24 = 199,065,600 \text{ bits/image} \]

Calculate Bits per Second

Finally, calculate the data rate by determining how many bits are sent per second. There are 50 images per second, so multiply the bits per image by the number of images per second.\[ 199,065,600 \times 50 = 9,953,280,000 \text{ bits/second} \]

Key concepts

Optical Fiber Transmission

Optical fiber transmission is a method to transport data as light signals through fibers made of glass or plastic. It is a highly efficient way to send large amounts of data over long distances quickly.
Optical fibers are thin and flexible, allowing them to be installed easily. They can handle a tremendous amount of data, which is perfect for high-demand applications like video streaming and high-resolution image transmission.
The ability to send data in the form of light pulses makes optical fibers far superior to older methods like copper wires, which rely on electrical signals that can degrade over distances. This is why optical fibers are the backbone of modern telecommunications networks.

• High capacity for data transmission.
• Excellent for long-distance communication.
• Reduced signal degradation over distance.

Pixel Bit Depth

Pixel bit depth determines color precision and is vital in digital imaging. Each pixel's color is represented by a specific number of bits. A higher bit depth permits more colors and finer shading, creating richer images.
In the exercise scenario, each pixel is represented by 24 bits, which is standard for color images. This provides 8 bits per color channel—red, green, and blue, allowing for over 16 million colors (calculated as \(2^{24}\)).
Understanding pixel bit depth helps in calculating data rates because it directly influences how much data each image requires.

• Essential for color accuracy.
• Each additional bit doubles color possibilities.
• Higher bit depth equals higher data requirements.

Image Data Transport

Image data transport refers to the movement of digital image data from one place to another. With contemporary needs for high-resolution image transfer, understanding how data is managed and transported efficiently is critical.
High-resolution images, like those in the problem where the entire screen is transmitted at once, require careful calculation of data rates. This ensures that the images move smoothly without latency.
Calculating image data transport often involves strategies like compression to reduce data size while maintaining quality and utilizing fast transmission mediums like optical fibers.

• Involves moving large quantities of data.
• Compression can ease transport needs.
• Critical for real-time applications such as video streaming.

Screen Resolution

Screen resolution refers to the number of distinct pixels that an image can display. A higher resolution represents more pixels in a given area, leading to clearer and more detailed images.
In the exercise, the screen resolution is \(3840 \times 2160\), known as 4K, meaning it has over 8 million pixels. High screen resolutions demand higher data rates because more pixels need to be processed and transmitted.
Understanding screen resolution is essential for professionals working with graphics, video production, and any technology involving displays, as it impacts the quality and the data it will consume during transport.

• The higher the resolution, the sharper the image.
• Impacts data rates and processing needs.
• Commonly expressed in terms (e.g., 4K, Full HD).