Ok, I'll solve Both situations... just, one situation will be more realistic.
Sorry for this long post ahead of time.
Ok, it really depends on what type of computer you consider normal. Mine is a 3Ghz processor x2 (Dual core); so, effectively, it is 6Ghz of processing power.
And when I mean power I mean SPEED. Each line of code in a program takes roughly 2-5 cycles to process the code segment. This is for Assembly language. An anagram decoder takes about 50 lines of code give or take. it is a rough estimate based off researching internet. This is for a Java code. Which is a higher level language but works the same.
Lets assume it to be 50 lines with 4 cycles each for the line. Also, there are loops in the code which a particular part is repeated over and over with a few lines. Lets assume this repetition is about 10 lines of code (this is where the 256! or the 256 makes a BIG difference in time.).
Now when I talk about cycles, I'm talking about the clock frequency, or the time between periods of a processors crystal oscillator (it generates the clock frequency in lame terms).
Lets use my computer as a common computer.
It has 6Ghz or (1/6GHz = 16.6667nano-seconds/cycle).
If 256!:
NOTE: c = cycles, s = seconds
I’ll use deciBels because it is simpler math and easier to convert to and fro.
1/6GHz = 16.6667ns/cycle
log(16.6667E-9) = -9.77815dBs/c
256! = 8.57818E506 or 8.57818 x 10^506 (HUGE NUMBER)
log(8.57818E506) = 506.933 <<<<See? Logarithms are so much easier.
Doing Math....
506.933 + 1 = 507.933dBc NOTE: the 1 is = to the *10 lines. If you understand math. You'll understand the basics of logarithms.
507.933dBc + -9.77815dBs/c = 498.155dBs
1.42889E498 seconds
4.54344E487 millenniums to decipher the anagram.
IF 256:
(256*10)c + 40c = 2600 cycles.
16.6667ns/cycle * 2600 cycles = 433.333ns to decode the anagram.
Note: I could have the time wrong. Because I am sure that the signal is slowed down some during the process of the computer. Plus, the computer is not SOLELY processing this program. It is using other programs in between this one. I am going to check with my teacher at school for this question. This is where baud rates are required to calculate the exact processing time.