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Thus the amplitude of each sample pulse in Fig. 327 represents a RANGE of possible values of v t , in accordance with the given table. Take, for example, time t 9 in Fig. 327. According to Fig. 327, v t 3 volts at t 9; actually, however, inspection of the table shows that the value of v t could be ANY VALUE in the range from 3 to 4 volts. This is, of course, just an illustration, and we would generally require greater accuracy in our work. We might, for example, require that the pulse amplitudes be broken down into, say, 32 di erent ranges ( quantization levels ) for greater accuracy. There is, however, always some amount of quantization error produced. The amount of such error allowed depends, of course, upon the particular application. The third and nal step is to encode the quantized PAM signal of Fig. 327 into a PCM signal, which is a signal in which ONLY TWO DIFFERENT PULSE CONDITIONS, on or o ( 1 or 0 ), have to be detected, regardless of the di erent pulse

amplitudes actually present in Fig. 327. This is done by representing each quantized level by a speci ed binary number, all pulses in the binary numbers having the same amplitude. Thus, in PCM it will not be necessary to detect di erent pulse amplitudes, but only if a pulse is present or not present, 1 or 0. Let us take the case of Fig. 327 as an example, as follows. As stated above, in PCM each of the various amplitude levels in the quantized sampled form of the analog signal is to be represented by a speci c binary number. Since there are 8 di erent voltage levels possible, including zero, in Fig. 327, this will require the use of 8 binary numbers of 3 binary digits each; thus

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236 237 237 238 239 240 242 243 246 250 250 251 255 257 258 262 262 263 263 268 269 270 270 271 271 272 274 276

Pulse amplitude 0 1 2 3 Binary form 000 001 010 011 Pulse amplitude 4 5 6 7 Binary form 100 101 110 111

The above information, in binary-coded form (PCM), can be basically represented (for t 1 through t 6) as shown in Fig. 328.

logFileWriter.println(url); } catch (Exception e) { showError("Unable to log match."); } } // Verify URL format. private URL verifyUrl(String url) { // Only allow HTTP URLs. if (!url.toLowerCase().startsWith("http://")) return null; // Verify format of URL. URL verifiedUrl = null; try { verifiedUrl = new URL(url); } catch (Exception e) { return null; } return verifiedUrl; } // Check if robot is allowed to access the given URL. private boolean isRobotAllowed(URL urlToCheck) { String host = urlToCheck.getHost().toLowerCase(); // Retrieve host's disallow list from cache. ArrayList disallowList = (ArrayList) disallowListCache.get(host); // If list is not in the cache, download and cache it. if (disallowList == null) { disallowList = new ArrayList(); try { URL robotsFileUrl = new URL("http://" + host + "/robots.txt"); // Open connection to robot file URL for reading. BufferedReader reader = new BufferedReader(new InputStreamReader( robotsFileUrl.openStream())); // Read robot file, creating list of disallowed paths.

The advantage of PCM is its great freedom from the e ects of noise. This is because, in order to extract the information from such a signal it is only necessary to determine whether a pulse is PRESENT or NOT PRESENT; that is, it is not necessary to know the exact amplitudes or shapes of the pulses. Thus, as long as the pulse amplitudes remain reasonably larger than the noise, the binary numbers, which represent the amplitudes of the sampled values of v t , can be recovered.

It should be noted that the use of PCM to transmit information at a high rate requires that the equipment have wide bandwidth. This is to be expected, because, as we know, a wide bandwidth is required for the fast transmission of pulses through networks. Now let s consider some of the algebra associated with PCM. To do this, it will be helpful to begin with a block diagram of the circuitry required to generate a PCM signal. Such a diagram is shown in Fig. 329, with explanation as follows.

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