10. In an image compression system 16384 bits are used to represent 256 × 256 image with 256 gray levels. What is the compression ratio for this system ?
(A) 1
(B) 2
(C) 4
(D) 8
Ans:- 
Explanation:-
Number of bits required to store a 256 X 256 image with 256 gray levels is.
256 gray levels = 28
=8 bits
Therefore 256 * 256 * 8 = 524,288 bits
The ratio of the original(uncompressed) image to the compressed image is referred to as the Compression Ratio CR.
CR = Uncompressed image size/Compressed image size
Uncompressed image size for the given data above= 524,288 bits
Compressed image size as given in the question = 16384 bits
Therefore, compression ratio = 524,288/16384 = 32
I am not converting the values into bytes.
There is no option called 32 in the answer at all. The solution website for June 2012 says option B which is 2. The same question is found in another place and the solution there is 8 but no explanation provided. If anyone can provide an explanation as to how 8 is the answer it will be great. I have got the value 32. So i am not choosing any option as the answer.
(A) 1
(B) 2
(C) 4
(D) 8
Ans:- 
Explanation:-
Number of bits required to store a 256 X 256 image with 256 gray levels is.
256 gray levels = 28
=8 bits
Therefore 256 * 256 * 8 = 524,288 bits
The ratio of the original(uncompressed) image to the compressed image is referred to as the Compression Ratio CR.
CR = Uncompressed image size/Compressed image size
Uncompressed image size for the given data above= 524,288 bits
Compressed image size as given in the question = 16384 bits
Therefore, compression ratio = 524,288/16384 = 32
I am not converting the values into bytes.
There is no option called 32 in the answer at all. The solution website for June 2012 says option B which is 2. The same question is found in another place and the solution there is 8 but no explanation provided. If anyone can provide an explanation as to how 8 is the answer it will be great. I have got the value 32. So i am not choosing any option as the answer.
Number of bits required to store a 256 X 256 image with 256 gray levels is.
ReplyDelete256 gray levels = 28
=8 bits
Therefore (256 * 256 * 8)/8 = 65536 bits
The ratio of the original(uncompressed) image to the compressed image is referred to as the Compression Ratio CR.
CR = Uncompressed image size/Compressed image size
Uncompressed image size for the given data above= 65536 bits
Compressed image size as given in the question = 16384 bits
Therefore, compression ratio = 65536/16384 = 4
The Option is C
Why divide by 8
Delete256is 2power8
DeleteSo 2power8 x 2power8x 8bits to rep color so total bits 2power19bits and compression required 2 power 15
2power19 divided by 2power15 ans is 4
Why it has been divided by again 8
ReplyDeleteIf compressed image size may in bytes then uncompressed image size can be converted into bytes dividing by 8 and compression ratio will be 4.
ReplyDelete