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Binary digit

Rather than being defined by lengthy explicit listings of their local action, rules are instead conventionally identified by a compact code. If the bottom eight binary digits of the r = 1 mod 2 rule in the example cited above are interpreted as the binary representation of a decimal number, then the code, i [ 2], is given by that base-10 equivalent ... [Pg.44]

This method has very little other than its simplicity to recommend it in the form just described. But when a binary base is used, the corresponding procedure is to bisect the interval successively. Each bisection determines one additional binary digit to the approximation, it requires only the evaluation of the function, and the method is often efficient and accurate. The principle is used by Givens (Section 2.3) in finding the roots of a tridiagonal symmetric matrix. [Pg.81]

Binary Data Source 1 Binary Triple 3 Binary Noisy Binary Data Channel Majority Decision on 3 Binary Digits Destination... [Pg.191]

In Pig. 4-lc, both the input and the output from the coder are binary sequences, but if planes are spotted only rarely, then the output will contain many fewer binary digits than the input. The theory developed later will show exactly how many binary digits are required from the coder. The important point here is that a reduction is possible and that it depends on the frequency (or probability) of l s in the input data. [Pg.192]

In Pig. 4-ld, the input and output from the coder are again binary digits, but the output contains 3 digits for every one digit at the input so as to correct errors on the channel. [Pg.192]

In the foregoing analysis of these three systems, we observe that the particular nature of the information being transmitted is irrelevant. In Pig. 4-lb, we were unconcerned with the names of the characters on the teletypewriter and with the nature of the pulses associated with the binary digits. The only quantity of interest was the size of the two alphabets. Similarly, in Fig. 4-lc, we were unconcerned with whether the radar was spotting planes or clouds we were concerned only with the size of the alphabet (binary), and with the frequency of occurrence of the symbols in the source alphabet. Finally, in Pig. 4-ld, the- relevant quantities were the number of channel symbols per source symbol and the frequency of errors on the channel. [Pg.192]

The name entropy is used here because of the similarity of Eq. (4-6) to the definition of entropy in statistical mechanics. We shall show later that H(U) is the average number of binary digits per source letter required to represent the source output. [Pg.196]

As an example of self information and entropy, consider the ensemble, U, consisting of the binary digits, 0, and 1. Then if we letp = Pr(l),... [Pg.197]

It is important to note in Theorem 4-2 that we could code a source into H(U) binary digits per symbol only when some arbitrarily small but non-zero error was tolerable. There are MN different N length sequences of symbols from an alphabet of M symbols and if no error is tolerable, a code word must be provided for each sequence. [Pg.200]

The average number of binary digits per source sequence is given by... [Pg.201]

Note that if the self information of each sequence can be made equal to the number of binary digits in its code word, then Nb = NH(U) thus the self information of a sequence in bits is the number of binary digits that should ideally be used to represent the sequence. [Pg.203]

Dividing Eqs. (4-19) and (4-20) by N, we see that the average number of binary digits per source symbol for the best prefix condition code satisfies... [Pg.203]

Assign a 1 as the last binary digit of the code word corresponding to the least probable source sequence, and a 0 as the last binary digit of the next to least probable source sequence. [Pg.204]

Suppose now that we had some other source of entropy R < R nats per channel symbol. We know from Theorem 4-2 that this source can be coded into binary digits as efficiently as desired. These binary digits can then be coded into letters of the alphabet %, , uM. Thus, aside from the equal probability assumption for the M letter source, our results are applicable to any source. [Pg.220]

Bernoulli s method, 79 Konig s Theorem and Hadahiard s generalization, 81 Bethe, H. A., 641 Bethenod, T., 380 Bifurcation, 342 diagram, 342 first kind, 339 point, 342 second kind, 339 theory of, 338 value, 338 Binary digits... [Pg.770]

While floating-point values are used to construct the strings in most scientific applications, in some types of problem the format of the strings is more opaque. In the early development of the genetic algorithm, strings were formed almost exclusively out of binary digits, which for most types of problem are more difficult to interpret letters, symbols, or even virtual objects... [Pg.118]

Applying one-point crossover at a randomly chosen position, the thirty-second binary digit in each string, we get the two new strings ... [Pg.152]

Binary digital images are obtained from the set of scalar data by thresholding. In the intensity level of a raw image, cf>(r) varies between 4>mm and ( )m ix. [Pg.192]

Computers contain read-only memory whose contents are permanent (i.e., can only be read and not written to by the user) along with random access memory that can both be read from and written to by the user. The basic computing unit is a bit (b), which stands for binary digit 8 bits comprise a byte (B). Table 3.5 illustrates calculation of computer memory bytes, i.e., the number of locations that can be addressed. [Pg.127]

In any computer, the most fundamental unit of information is considered the binary digit, otherwise known as a bit. In... [Pg.2]

Just a few years ago, the so-called C3 laser (cleaved-coupled-cavity) appeared, wherein the alignment of two conventional semiconductor lasers yields a beam of exceptional purity that enables communication systems to send signals at rates as great as billions of bits, or binary digits per second. Just as recently as the late 1980s, commercial lightwave systems were limited to somewhat less than 2 million bits per second, but nevertheless a rate that permits the transmission of 24,000 simultaneous telephone calls on a single pair of fibers. [Pg.1156]

BIT (b). A unit of information, generally represented by a pulse. A bit is a binary digit, i.e., a 1 or 0 in computer technology. (In information theory, the bit is the smallest possible unit of information.)... [Pg.1643]

Once the key has been safely delivered to the recipient and the plaintext has been encrypted any brute force attack on the cryptotext must deal with a huge number of possible keys. For example if the key has 128 binary digits the number of all possible keys is approximately 1038. [Pg.327]


See other pages where Binary digit is mentioned: [Pg.768]    [Pg.367]    [Pg.192]    [Pg.195]    [Pg.198]    [Pg.198]    [Pg.201]    [Pg.201]    [Pg.219]    [Pg.773]    [Pg.154]    [Pg.529]    [Pg.355]    [Pg.418]    [Pg.22]    [Pg.170]    [Pg.210]    [Pg.447]    [Pg.1157]    [Pg.540]    [Pg.557]    [Pg.711]    [Pg.236]    [Pg.529]    [Pg.239]    [Pg.303]    [Pg.65]   
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See also in sourсe #XX -- [ Pg.4 , Pg.42 , Pg.43 , Pg.313 ]

See also in sourсe #XX -- [ Pg.588 ]

See also in sourсe #XX -- [ Pg.96 ]




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