Suppose that the scientist has 100 coins, and he is told that he has a
1 in 64 chance of opening the door if he tosses the correct number of coins and enters an
H or T into the computer. He is told not to toss all 100 coins because the combination for
the door is not that long. He is also told that the door only has one correct combination.
How does the scientist figure out how many coins to toss? He needs to convert
the odds of opening the door into an equivalent number of bits. One way is trial and
error. He can compose a table like table 1.1. From this table, it is clear that if the
scientist tosses 6 coins, he will have a 1 in 64 chance of opening the door.
Table 1.1- Information Contained in Coins
Number of Coins |
information in bits |
possible outcomes |
Odds |
0 |
0 |
20=1 |
1 in 1 |
1 |
1 |
21=2 |
1 in 2 |
2 |
2 |
22=2x2 =4 |
1 in 4 |
3 |
3 |
23=2x2x2 =8 |
1 in 8 |
4 |
4 |
24=2x2x2x2 =16 |
1 in 16 |
5 |
5 |
25=2x2x2x2x2=32 |
1 in 32 |
6 |
6 |
26= 2x2x2x2x2x2=64 |
1 in 64 |
7 |
7 |
27 =2x2x2x2x2x2x2=128 |
1 in 128 |
8 |
8 |
28=2x2x2x2x2x2x2x2 =256 |
1 in 256 |
13 |
13 |
213 = 2x2x2x2.....x2= 8192 |
1 in 8192 |
Notice that there is a definite relationship between the number of bits in
the door’s combination and the odds that the scientist will open the door.
Probability theory and information theory are closely related.
Next: mathemtical definition of
information
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