Numericals – CG
November 26th, 2009Consider three different raster systems with resolutions of 640 x 480, 1280 x 1024, and 2560 x 2048.
a) What size is frame buffer (in bytes) for each of these systems to store 12 bits per pixel?
Because eight bits constitute a byte, frame-buffer sizes of the systems are as follows:
640 x 480 x 12 bits / 8 = 450KB;
1280 x 1024 x 12 bits / 8 = 1920KB;
2560 x 2048 x 12 bits / 8 = 7680KB;
b) How much storage (in bytes) is required for each system if 24 bits per pixel are to be stored?
Similarly, each of the above results is just doubled for 24 (12×2) bits of storage per pixel.
Consider two raster systems with the resolutions of 640 x 480 and 1280 x 1024.
a) How many pixels could be accessed per second in each of these systems by a display controller that refreshes the screen at a rate of 60 frames per second?
Since 60 frames are refreshed per second and each frame consists of 640 x 480 pixels, the access rate of such a system is (640 x 480) * 60 = 1.8432 x 107 pixels/second.
Likewise, for the 1280 x 1024 system, the access rate is (1280 x 1024) * 60 = 7.86432 x 107 pixels/second.
b) What is the access time per pixel in each system?
According to the definition of access rate, we know that the access time per pixel should be 1/(access rate). Therefore, the access time is around 54 nanoseconds/pixel for the 640 x 480 system, and the access time is around 12.7 nanoseconds/pixel for the 1280×1024 system.
Consider a raster system with the resolution of 1024 x 768 pixels and the color palette calls for 65,536 colors. What is the minimum amount of video RAM that the computer must have to support the above-mentioned resolution and number of colors?
Recall that the color of each pixel on a display is represented with some number of bits. Hence, a display capable of showing up to 256 colors is using 8 bits per pixels (i.e. “8-bit color”).
Notice first that the color palette calls for 65,536 colors. This number is but 216 , which implies that 16 bits are being used to represent the color of each pixel on the display. The display’s resolution is 1024 by 768 pixels, which implies that there is a total of 786,432 (1024 × 768) pixels on the display. Hence, the total number of bits required to display any of 65,536 colors on each of the screen’s 786,432 pixels is 12,582,912 (786,432 × 16). Dividing this value by 8 yields an answer of 1,572,864 bytes. Dividing that value by 1,024 yields an answer of 1,536 KB. Dividing that value by 1,024 yields an answer of 1.5 MB.