Search results
Results From The WOW.Com Content Network
If a message recipient may expect any one of N possible messages with equal likelihood, then the amount of information conveyed by any one such message is quantified as log 2 N bits. [86] Lyapunov exponents use logarithms to gauge the degree of chaoticity of a dynamical system. For example, for a particle moving on an oval billiard table, even ...
Infrequently occurring messages contain more information than more frequently occurring messages. It can also be shown that a compound message of two (or more) unrelated messages would have a quantity of information that is the sum of the measures of information of each message individually.
Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory. In computer science, they count the number of steps needed for binary search and related algorithms.
The different units of information (bits for the binary logarithm log 2, nats for the natural logarithm ln, bans for the decimal logarithm log 10 and so on) are constant multiples of each other. For instance, in case of a fair coin toss, heads provides log 2 (2) = 1 bit of information, which is approximately 0.693 nats or 0.301 decimal digits.
If the receiving entity had previously known the content of a message with certainty before receiving the message, the amount of information of the message received is zero. Only when the advance knowledge of the content of the message by the receiver is less than 100% certain does the message actually convey information.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [b] Thus, log tables need only show the fractional part. Tables of common logarithms ...