A graphic display system has a frame buffer that is 640 pixels wide, 480 pixels high and 1 bit of color depth. If the access time for each pixel on the average is 200 nanoseconds, then the refresh rate of this frame buffer is approximately:
16 frames per second
Understanding Frame Buffer Refresh Rate
The question asks us to determine the refresh rate of a graphic display system based on its frame buffer dimensions, color depth, and pixel access time. The refresh rate tells us how many times the entire image on the screen is updated per second. This is directly related to the total time it takes to read out all the pixel data from the frame buffer to display it.
Calculating Total Pixels in the Frame Buffer
The frame buffer stores the data for each pixel displayed on the screen. The size of the frame buffer in terms of pixels is given by its width and height.
- Width = 640 pixels
- Height = 480 pixels
The total number of pixels is the product of the width and height.
Total Pixels = Width $\times$ Height
Total Pixels = $640 \times 480$
Total Pixels = $307200$ pixels
The color depth (1 bit) affects the amount of memory needed per pixel, but for calculating the time to read *all* pixels sequentially, we only need the total count of pixels.
Calculating Total Time for One Frame Refresh
We are given the average access time for each pixel. To refresh the entire screen, the system needs to access data for every pixel in the frame buffer.
- Average pixel access time = 200 nanoseconds (ns)
First, let's convert the pixel access time to seconds:
$1$ nanosecond $= 10^{-9}$ seconds
$200$ nanoseconds $= 200 \times 10^{-9}$ seconds
The total time required to read all pixels for one frame refresh is the total number of pixels multiplied by the time it takes to access each pixel.
Total time per frame = Total Pixels $\times$ Average pixel access time
Total time per frame = $307200 \times (200 \times 10^{-9})$ seconds
Total time per frame = $61440000 \times 10^{-9}$ seconds
Total time per frame = $0.06144$ seconds
Determining the Frame Buffer Refresh Rate
The refresh rate is defined as the number of frames that can be displayed per second. If it takes $T$ seconds to display one frame, then the number of frames that can be displayed in one second is $1/T$.
Refresh Rate = $1 / (\text{Total time per frame})$
Refresh Rate = $1 / 0.06144$ frames per second
Refresh Rate $\approx 16.277$ frames per second
Comparing with Options
Now we compare our calculated refresh rate with the given options:
| Option | Refresh Rate (fps) |
|---|---|
| 1 | 16 |
| 2 | 19 |
| 3 | 21 |
| 4 | 23 |
The calculated value of approximately 16.277 frames per second is closest to 16 frames per second.
Summary of Calculation for Frame Buffer Refresh
Here's a summary of the steps:
- Calculate total pixels: $640 \times 480 = 307200$ pixels.
- Convert pixel access time to seconds: $200 \text{ ns} = 200 \times 10^{-9} \text{ s}$.
- Calculate total time per frame: $307200 \times (200 \times 10^{-9}) = 0.06144 \text{ s}$.
- Calculate refresh rate: $1 / 0.06144 \approx 16.277 \text{ fps}$.
Conclusion on Refresh Rate Calculation
Based on the calculations, the refresh rate of the frame buffer is approximately 16 frames per second.
Revision Table: Frame Buffer and Refresh
| Term | Definition/Concept | Relevance to Question |
|---|---|---|
| Frame Buffer | Memory area holding pixel data for a display. | Its dimensions determine total pixels. |
| Resolution | Width $\times$ Height of the display in pixels. | Defines the size of the frame buffer in pixels (e.g., 640x480). |
| Color Depth | Number of bits per pixel representing color information. | Affects memory size, but not directly access time per pixel count. |
| Pixel Access Time | Average time to read or write data for one pixel. | Crucial for calculating total refresh time. |
| Refresh Rate | Number of times the screen is updated per second (in Hz or fps). | The quantity we are calculating. Depends on total pixels and pixel access time. |
Additional Information: Graphics System Concepts
Understanding how graphic display systems work involves several components and concepts:
- Pixel: The smallest addressable element on a display screen.
- Frame: A single still image displayed on the screen.
- Scanline: A single row of pixels on the display. Display devices typically draw images scanline by scanline.
- Vertical Sync (V-sync): A signal that synchronizes the drawing of a new frame with the display's refresh cycle, preventing screen tearing.
- Bandwidth: The rate at which data can be read from the frame buffer and sent to the display controller. A higher refresh rate requires higher bandwidth.
- Memory Type: The type of memory used for the frame buffer (e.g., VRAM, DRAM) affects pixel access time and overall performance.
The refresh rate is a critical performance metric for display systems, affecting perceived motion smoothness and flicker.
Important Questions from Graphics Systems
If we want to resize a 1024 × 768 pixels image to one that is 640 pixels wide with the same aspect ratio, what would be the height of the resized image?
Consider a raster system with resolution 640 by 480. What size is frame buffer (in bytes) for this system to store 12 bits per pixel?
Which component of CRT regulate the intensity of electron beam?
The duration of phosphorescence exhibited by a phosphor is known as ______.
- Which of the following are applicable to programming graphics (pre-design phase) during design development process?
(a) Graphic worksheets
(b) Analysis cards
(c) Variety of matrics
(d) Bubble diagram
Choose the correct option :
