Pop Quiz Solutions
Posted by Janet on May 18, 2008
The winner of the pop quiz has been contacted by e-mail today. The answers I was looking for were 913.1 kilobytes for question 1 and 3.57 megabytes for question 2. I have accepted a few other reasonable responses as well. These numbers can either be calculated or looked up in Photoshop by entering the parameters.
Here is the most detailed (and correct) response I received. This reader was unfortunately not the winner, but he gets credit for showing the calculation:
1). Assume that there are 256 greyscale levels. This means that each dot
takes up log2(256) = 8 bits = 1 byte of storage space. At 100 dpi (where
dpi is a linear measure), the number of dots in one square inch is 100 x 100
= 10000 dots per square inch.
An 8.5″x11″ image occupies 93.5 square inches. The number of dots in this
space is therefore 93.5*10^4 = 9.35*10^5. At 1 byte per dot, this
corresponds to 9.35*10^5 bytes. Under the strict definition of 2^10 bytes
per kilobyte, this becomes approximately:
(9.35*10^5)/(2^10) = 913.09 kilobytes.
2). For a CMYK image, assume 8 bits each are allocated to the C,M,Y, and K
channels for a total of 32 bits = 4 bytes per dot. As calculated in (1), an
8.5″x11″ image has 9.35*10^5 dots total. This results in an image size of:
9.35*10^5*4 = 3740000 bytes
Under the convention that 2^20 bytes = 1 megabyte, this is:
3740000/(2^20) = 3.57 megabytes