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Homework Statement
PROBLEM STATEMENT:
Show that with an n × n pixel grid, where each pixel can take on m intensity levels, we can approximate n × n ×(m – 1) + 1 overall intensity levels.
TEXTBOOK'S SOLUTION TO THE PROBLEM:
Since the n ×n pixels can be set to a non-zero intensity value one after another to produce n ×n overall intensity levels, and there are m MINUS 1 non-zero intensity levels for the individual pixels, we can approximate a total of n × n × (m – 1) non-zero overall intensity levels. Finally, we need to add one more overall intensity level that corresponds to zero intensity (all pixels off).
Homework Equations
According to the solution of the textbook: Approximate amount of overall intensity levels = n × n × (m – 1) + 1
The Attempt at a Solution
(Having researched, I found that "a pixel intensity value describes how bright that pixel is and/or what color it should be.")
Why is an "overall intensity level" just one of the n × n pixels as a non-zero intensity, with the rest as zero? Shouldn't there be a huge amount of combinations, like, for example, pixel 0 and pixel 1 having non-zero values or pixel n – 2, n – 1 and n each having non-zero pixels, etc.? In other words, shouldn't the answer be something like "n × n choose m" = (n×n)Cm?
Any help in getting me to fully understand the problem and its solution would be GREATLY appreciated!
P.S.
Why is the answer that the textbook gives an approximation?
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