urement one can make. This concept is encapsulated in the familiar coin-tossing game. Since a coin has two sides (heads and tails), the probabilities that it falls on either side are equal (overlooking here any other material possibility). This feature is translated mathematically into the relation p(x = heads) = p(x = tails) = 1/2. Consistent with the definition in Eq. (3.3), the information that one gets from tossing a coin is I(x) = log[p(x)] or, in this case, I(heads) = I (tails) = - log(1/2) = 0.693 nat. We may choose logarithms in base 2 to make this information value an integer, namely, defining6 (3.8) which givesI(heads) =I(tails)=-log2(2-1)=-(1) = log2(2) 1. The unit of this new measure of information is the bit, as short for binary digit. What a bit represents is, thus, the exact amount of elementary information necessary to describe the outcome of a coin tossing. The property I = 1 bit means that the message used to transmit the information only requires a single symbol, out of a source of 21 = 2 possible symbols. We can thus use any character pair, for instance, tails = 0 and heads = 1, for simplicity. The conclusion is that the smallest information message is a bit, namely, containing either 0 or 1 as a symbol. The information regarding the outcome of the coin tossing can thus be communicated through a single message bit, which represents the minimum amount of measurable information. 6 The conversion between natural and base-2 logarithms is given by the relation log2 x = log x/log2 1.442 log x. We could also have used base-3 or base-4 logarithms, defining the "trit" or the "quad," as representing three-valued or four-valued units of information. But the bit is the most elementary unit that cannot be sliced down into a smaller dimension. Measuring information If we toss the coin several times in a row, the information concerning the succession of outcomes is described by a string of as many single bits. For instance, the message consisting in the string 1101001101 means that the first two outcomes are