Understanding Frame Buffer Size in Raster Systems

In computer graphics, a raster system represents an image as a grid of individual pixels. The frame buffer is a dedicated memory area used to store the image data for display on the screen. The size of the frame buffer depends on the resolution of the display and the number of bits used to represent the color of each pixel (bits per pixel).

The question asks for the size of the frame buffer in bytes for a raster system with a resolution of 640 by 480 pixels and 12 bits per pixel.

Key Components for Calculation

• Resolution: 640 pixels (width) by 480 pixels (height). This tells us the total number of pixels on the screen.
• Bits per pixel: 12 bits. This tells us how much memory is needed to store the color information for a single pixel.
• Units: We need the final size in bytes, and then convert to kilobytes for the options provided.

Calculating Frame Buffer Size

To find the total size of the frame buffer, we first calculate the total number of pixels, then the total number of bits required, and finally convert the total bits into bytes and then kilobytes.

Step 1: Calculate the Total Number of Pixels

The total number of pixels is the product of the width and height resolution.

Total Pixels = Resolution Width $\times$ Resolution Height

Total Pixels = $640 \times 480$

Total Pixels = $307,200$ pixels

Step 2: Calculate the Total Number of Bits Required

Multiply the total number of pixels by the number of bits used per pixel.

Total Bits = Total Pixels $\times$ Bits per Pixel

Total Bits = $307,200 \times 12$ bits

Total Bits = $3,686,400$ bits

Step 3: Convert Total Bits to Bytes

There are 8 bits in 1 byte. To convert bits to bytes, divide the total number of bits by 8.

Total Bytes = Total Bits / 8

Total Bytes = $3,686,400$ bits / 8 bits/byte

Total Bytes = $460,800$ bytes

Step 4: Convert Total Bytes to Kilobytes

There are 1024 bytes in 1 kilobyte (KB). To convert bytes to kilobytes, divide the total number of bytes by 1024.

Total Kilobytes = Total Bytes / 1024

Total Kilobytes = $460,800$ bytes / 1024 bytes/KB

Total Kilobytes = $450$ KB

The size of the frame buffer required for a raster system with 640 by 480 resolution and 12 bits per pixel is 450 kilobytes.

Result Summary

Let's summarize the steps and results in a table:

Based on our calculation, the frame buffer size is 450 kilobytes.

Revision Table: Raster Graphics Concepts

Additional Information: Memory Units and Color Depth

Understanding memory units and color depth is crucial for frame buffer size calculations in computer graphics and display systems.

• Memory Units: Digital information size is measured in bits and bytes. 1 byte = 8 bits. Larger units include Kilobytes (KB), Megabytes (MB), Gigabytes (GB), etc. In computer systems, KB is typically $2^{10}$ bytes (1024 bytes), MB is $2^{20}$ bytes ($1024 \times 1024$ bytes), and so on.
• Color Depth (Bits per Pixel):
  • 1 bit per pixel: Black and white (monochrome).
  • 8 bits per pixel: Allows for 256 different colors (often indexed colors).
  • 16 bits per pixel: High color, typically 5 bits for Red, 6 bits for Green, 5 bits for Blue (5-6-5 format), allowing $2^{16} = 65,536$ colors.
  • 24 bits per pixel: True color, typically 8 bits each for Red, Green, and Blue ($8+8+8 = 24$), allowing $2^{24} \approx 16.7$ million colors.
  • 32 bits per pixel: True color with an 8-bit alpha channel (transparency information), $8+8+8+8=32$.
  • The question uses 12 bits per pixel, which might be an intermediate or custom color depth configuration.

The frame buffer stores the color value for each pixel. The higher the resolution and the higher the bits per pixel, the larger the frame buffer size required, leading to higher memory costs and potentially affecting display performance.