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<h2 id="information-theory">Information theory</h2> <p>In 1928, <a href="/facts/Ralph_Hartley/oVKw8QUK">Ralph Hartley</a> observed a fundamental storage principle,<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> which was further formalized by <a href="/facts/Claude_Shannon/EremsCws">Claude Shannon</a> in 1945: the information that can be stored in a system is proportional to the <a href="/facts/Logarithm/QeXaV97q">logarithm</a> of <i>N</i> possible states of that system, denoted log<i>b</i> <i>N</i>. Changing the base of the logarithm from <i>b</i> to a different number <i>c</i> has the effect of multiplying the value of the logarithm by a fixed constant, namely log<i>c</i> <i>N</i> = (log<i>c</i> <i>b</i>) log<i>b</i> <i>N</i>. Therefore, the choice of the base <i>b</i> determines the unit used to measure information. In particular, if <i>b</i> is a <a href="/facts/Positive_and_negative_numbers/LzErzCmI">positive</a> integer, then the unit is the amount of information that can be stored in a system with <i>b</i> possible states. </p><p>When <i>b</i> is 2, the unit is the <a href="/facts/Shannon_(unit)/VEevYzKM">shannon</a>, equal to the <a href="/facts/Information_content/EkUdL669">information content</a> of one "bit". A system with 8 possible states, for example, can store up to log2 8 = 3 bits of information. Other units that have been named include: </p> Base <i>b</i> = 3 the unit is called "<a href="/facts/Ternary_numeral_system/bMUfR74P">trit</a>", and is equal to log2 3 (≈ 1.585) bits.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> Base <i>b</i> = 10 the unit is called <i><a href="/facts/Decimal/7omfVNIM">decimal</a> <a href="/facts/Numerical_digit/JJdLBoGT">digit</a></i>, <i><a href="/facts/Hartley_(unit)/HHnoxYMR">hartley</a></i>, <i>ban</i>, <i>decit</i>, or <i>dit</i>, and is equal to log2 10 (≈ 3.322) bits.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> Base <i>b</i> = <i>e</i>, the <a href="/facts/Base_of_natural_logarithm/coEtSBk8">base of natural logarithms</a> the unit is called a <i><a href="/facts/Nat_(unit)/UgNgfVgI">nat</a></i>, <i>nit</i>, or <i>nepit</i> (from <a href="/facts/John_Napier/Wg0HAmq5">Neperian</a>), and is worth log2 <i>e</i> (≈ 1.443) bits.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> <p>The trit, ban, and nat are rarely used to measure storage capacity; but the nat, in particular, is often used in information theory, because natural logarithms are mathematically more convenient than logarithms in other bases. </p> <h2 id="units-derived-from-bit">Units derived from bit</h2> <p>Several conventional names are used for collections or groups of bits. </p> <h3>Byte</h3> <p>Historically, a <a href="/facts/Byte/BNHUp9Qq">byte</a> was the number of bits used to encode a <a href="/facts/Character_(computing)/X2zKLFFB">character</a> of text in the computer, which depended on computer hardware architecture, but today it almost always means eight bits – that is, an <a href="/facts/Octet_(computing)/dqCHsuUF">octet</a>. An 8-bit byte can represent 256 (28) distinct values, such as non-negative integers from 0 to 255, or <a href="/facts/Two%2527s_complement/xhjYpnsc">signed</a> integers from −128 to 127. The <a href="/facts/IEEE_1541-2002/pK1IxH49">IEEE 1541-2002</a> standard specifies "B" (upper case) as the symbol for byte (<a href="/facts/IEC_80000-13/k1nrIjMW">IEC 80000-13</a> uses "o" for octet in French, but also allows "B" in English). Bytes, or multiples thereof, are almost always used to specify the sizes of computer files and the capacity of storage units. Most modern computers and peripheral devices are designed to manipulate data in whole bytes or groups of bytes, rather than individual bits. </p> <h3>Nibble</h3> <p>A group of four bits, or half a byte, is sometimes called a <a href="/facts/Nibble/PUaqCEVw">nibble</a>, nybble or nyble. This unit is most often used in the context of <a href="/facts/Hexadecimal/02ohQW22">hexadecimal</a> number representations, since a nibble has the same number of possible values as one hexadecimal digit has.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> </p> <h3>Word, block, and page</h3> <p>Computers usually manipulate bits in groups of a fixed size, conventionally called <i><a href="/facts/Word_(computer_architecture)/2e5umRaj">words</a></i>. The number of bits in a word is usually defined by the size of the <a href="/facts/Register_(computing)/32RvbUdz">registers</a> in the computer's <a href="/facts/CPU/Jxp1bqMV">CPU</a>, or by the number of data bits that are fetched from its <a href="/facts/Main_memory/wPHKFpdx">main memory</a> in a single operation. In the <a href="/facts/IA-32/7yTv1aHH">IA-32</a> architecture more commonly known as x86-32, a word is 32 bits, but other past and current architectures use words with 4, 8, 9, 12, 13, 16, 18, 20, 21, 22, 24, 25, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 72<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> bits or others. </p><p>Some <a href="/facts/Machine_instruction/bgdQ1Fxf">machine instructions</a> and <a href="/facts/Computer_number_format/fmLUI4hh">computer number formats</a> use two words (a "double word" or "dword"), or four words (a "quad word" or "quad"). </p><p>Computer <a href="/facts/Memory_cache/gmJYN8wm">memory caches</a> usually operate on <i><a href="/facts/Block_(data_storage)/S3vT7c6N">blocks</a></i> of memory that consist of several consecutive words. These units are customarily called <i>cache blocks</i>, or, in <a href="/facts/CPU_cache/x8BYFcdv">CPU caches</a>, <i>cache lines</i>. </p><p><a href="/facts/Virtual_memory/Lw2GemF5">Virtual memory</a> systems partition the computer's <a href="/facts/Main_storage/wPHKFpdx">main storage</a> into even larger units, traditionally called <i><a href="/facts/Page_(computer_memory)/CNGruG1H">pages</a></i>. </p> <h3>Multiplicative prefixes</h3> <p>A unit for a large amount of data can be formed using either a metric or binary prefix with a base unit. For storage, the base unit is typically byte. For communication throughput, a base unit of bit is common. For example, using the metric <i>kilo</i> prefix, a <a href="/facts/Kilobyte/jIe6t4yv">kilobyte</a> is 1000 bytes and a <a href="/facts/Kilobit/I79XYhdw">kilobit</a> is 1000 bits. </p><p>Use of metric prefixes is common, but often inaccurate since binary storage hardware is organized with capacity that is a power of 2 – not 10 as the metric prefixes are. In the context of computing, the metric prefixes are often intended to mean something other than their normal meaning. For example, 'kilobyte' often refers to 1024 bytes even though the standard meaning of kilo is 1000. Also, 'mega' normally means one million, but in computing is often used to mean 220 = 1048576. The table below illustrates the differences between normal metric sizes and the intended size – the binary size. </p> <table><tbody><tr><th>Symbol</th><th>Prefix</th><th>Metric size</th><th>Binary size</th><th>Size difference</th></tr><tr><td>k</td><td>kilo</td><td>1000</td><td>1024</td><td>2.40%</td></tr><tr><td>M</td><td>mega</td><td>10002</td><td>10242</td><td>4.86%</td></tr><tr><td>G</td><td>giga</td><td>10003</td><td>10243</td><td>7.37%</td></tr><tr><td>T</td><td>tera</td><td>10004</td><td>10244</td><td>9.95%</td></tr><tr><td>P</td><td>peta</td><td>10005</td><td>10245</td><td>12.59%</td></tr><tr><td>E</td><td>exa</td><td>10006</td><td>10246</td><td>15.29%</td></tr><tr><td>Z</td><td>zetta</td><td>10007</td><td>10247</td><td>18.06%</td></tr><tr><td>Y</td><td>yotta</td><td>10008</td><td>10248</td><td>20.89%</td></tr><tr><td>R</td><td>ronna</td><td>10009</td><td>10249</td><td>23.79%</td></tr><tr><td>Q</td><td>quetta</td><td>100010</td><td>102410</td><td>26.77%</td></tr></tbody></table> <p>The <a href="/facts/International_Electrotechnical_Commission/hSK0kjwI">International Electrotechnical Commission</a> (IEC) issued a standard that introduces <a href="/facts/Binary_prefixes/oM3wgJgW">binary prefixes</a> that accurately represent binary sizes without changing the meaning of the standard metric terms. Rather than based on powers of 1000, these are based on powers of 1024 which is a power of 2.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> </p> <table><tbody><tr><th>Symbol</th><th>Prefix</th><th>Example</th><th>Size</th></tr><tr><td>Ki</td><td>kibi</td><td>kibibyte (KiB)</td><td>210, 1024</td></tr><tr><td>Mi</td><td>mebi</td><td>mebibyte (MiB)</td><td>220, 10242</td></tr><tr><td>Gi</td><td>gibi</td><td>gibibyte (GiB)</td><td>230, 10243</td></tr><tr><td>Ti</td><td>tebi</td><td>tebibyte (TiB)</td><td>240, 10244</td></tr><tr><td>Pi</td><td>pebi</td><td>pebibyte (PiB)</td><td>250, 10245</td></tr><tr><td>Ei</td><td>exbi</td><td>exbibyte (EiB)</td><td>260, 10246</td></tr><tr><td>Zi</td><td>zebi</td><td>zebibyte (ZiB)</td><td>270, 10247</td></tr><tr><td>Yi</td><td>yobi</td><td>yobibyte (YiB)</td><td>280, 10248</td></tr><tr><td>Ri</td><td>robi</td><td>robibyte (RiB)</td><td>290, 10249</td></tr><tr><td>Qi</td><td>quebi</td><td>quebibyte (QiB)</td><td>2100, 102410</td></tr></tbody></table> <p>The <a href="/facts/JEDEC_memory_standards/9Ps5DckI">JEDEC memory standard</a> JESD88F notes that the definitions of kilo (K), giga (G), and mega (M) based on powers of two are included only to reflect common usage, but are otherwise deprecated.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> </p> <h2 id="size-examples">Size examples</h2> <ul><li>1 bit: Answer to a yes/no question</li> <li>1 byte: A number from 0 to 255</li> <li>90 bytes: Enough to store a typical line of text from a book</li> <li>512 bytes = 0.5 KiB: The typical <a href="/facts/Disk_sector/V1R9Ivul">sector</a> size of an old style <a href="/facts/Hard_disk_drive/kekLSGSE">hard disk drive</a> (modern <a href="/facts/Advanced_Format/57nHzxUV">Advanced Format</a> sectors are 4096 bytes).</li> <li>1024 bytes = 1 KiB: A <a href="/facts/Block_(data_storage)/S3vT7c6N">block</a> size in some older <a href="/facts/UNIX/0pNL2seI">UNIX</a> <a href="/facts/Filesystem/FdPm90uc">filesystems</a></li> <li>2048 bytes = 2 KiB: A <a href="/facts/CD-ROM/JwuaYLJv">CD-ROM</a> sector</li> <li>4096 bytes = 4 KiB: A <a href="/facts/Memory_page/CNGruG1H">memory page</a> in <a href="/facts/X86/Kypq5fgu">x86</a> (since <a href="/facts/Intel_80386/ag5eSgWv">Intel 80386</a>) and many other architectures, also the modern <a href="/facts/Advanced_Format/57nHzxUV">Advanced Format</a> hard disk drive sector size.</li> <li>4 kB: About one page of text from a <a href="/facts/Novel/3Q8sXXLU">novel</a></li> <li>120 kB: The text of a typical pocket book</li> <li>1 MiB: A 1024×1024 pixel <a href="/facts/Bitmap/Fr80ySnT">bitmap</a> image with 256 colors (8 bpp color depth)</li> <li>3 MB: A three-minute <a href="/facts/Song/wm7uRPzQ">song</a> (133 kbit/s)</li> <li>650–900 MB – a CD-ROM</li> <li>1 GB: 114 minutes of uncompressed CD-quality audio at 1.4 Mbit/s</li> <li>16 GB: DDR5 DRAM laptop memory under $40 (as of early 2024)</li> <li>32/64/128 GB: Three common sizes of <a href="/facts/USB_flash_drive/Jv0qmTCF">USB flash drives</a></li> <li>1 TB: The size of a $30 hard disk (as of early 2024)</li> <li>6 TB: The size of a $100 hard disk (as of early 2022)</li> <li>16 TB: The size of a small/cheap $130 (as of early 2024) enterprise SAS hard disk drive</li> <li>24 TB: The size of $440 (as of early 2024) "video" hard disk drive</li> <li>32 TB: Largest <a href="/facts/Hard_disk_drive/kekLSGSE">hard disk drive</a> (as of mid-2024)</li> <li>100 TB: Largest commercially available <a href="/facts/Solid-state_drive/aMHBy8gU">solid-state drive</a> (as of mid-2024)</li> <li>200 TB: Largest solid-state drive constructed (prediction for mid-2022)</li> <li>1.6 PB (1600 TB): Amount of possible storage in one 2U server (world record as of 2021, using 100 TB solid-states drives).<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a></li> <li>1.3 ZB: Prediction of the volume of the whole internet in 2016</li></ul> <h2 id="obsolete-and-unusual-units">Obsolete and unusual units </h2> <p>Some notable unit names that are today obsolete or only used in limited contexts. </p> <ul><li>1 bit: unibit<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a><a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a></li></ul> <ul><li>2 bits: dibit,<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a><a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a><a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a><a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> crumb,<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> quartic digit,<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> quad, semi-nibble, nyp<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></li></ul> <ul><li>3 bits: tribit,<a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a><a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a> triad,<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a> triade<a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a><a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a></li></ul> <ul><li>4 bits: see <a href="/facts/Nibble/PUaqCEVw">nibble</a></li></ul> <ul><li>5 bits: pentad, pentade,<a class="footnote-ref" id="fnref:29" href="#fn:29"><sup>29</sup></a></li></ul> <ul><li>6 bits: byte (in early <a href="/facts/IBM/QszA7nwd">IBM</a> machines using <a href="/facts/Binary_Coded_Decimal/dWTaE7ES">BCD alphamerics</a>), hexad, hexade,<a class="footnote-ref" id="fnref:30" href="#fn:30"><sup>30</sup></a><a class="footnote-ref" id="fnref:31" href="#fn:31"><sup>31</sup></a> sextet<a class="footnote-ref" id="fnref:32" href="#fn:32"><sup>32</sup></a></li></ul> <ul><li>7 bits: heptad, heptade<a class="footnote-ref" id="fnref:33" href="#fn:33"><sup>33</sup></a></li></ul> <ul><li>8 bits: <a href="/facts/Octad_(computing)/dqCHsuUF">octad</a>,<a class="footnote-ref" id="fnref:34" href="#fn:34"><sup>34</sup></a> <a href="/facts/Octade_(computing)/dqCHsuUF">octade</a><a class="footnote-ref" id="fnref:35" href="#fn:35"><sup>35</sup></a></li></ul> <ul><li>9 bits: nonet,<a class="footnote-ref" id="fnref:36" href="#fn:36"><sup>36</sup></a> rarely used</li></ul> <ul><li>10 bits: declet,<a class="footnote-ref" id="fnref:37" href="#fn:37"><sup>37</sup></a><a class="footnote-ref" id="fnref:38" href="#fn:38"><sup>38</sup></a><a class="footnote-ref" id="fnref:39" href="#fn:39"><sup>39</sup></a><a class="footnote-ref" id="fnref:40" href="#fn:40"><sup>40</sup></a> decle<a class="footnote-ref" id="fnref:41" href="#fn:41"><sup>41</sup></a></li></ul> <ul><li>12 bits: <a href="/facts/Slab_(unit)/P4jCBhRE">slab</a><a class="footnote-ref" id="fnref:42" href="#fn:42"><sup>42</sup></a><a class="footnote-ref" id="fnref:43" href="#fn:43"><sup>43</sup></a><a class="footnote-ref" id="fnref:44" href="#fn:44"><sup>44</sup></a></li></ul> <ul><li>15 bits: parcel (on <a href="/facts/CDC_6600/QpnT1Ltl">CDC 6600</a> and <a href="/facts/CDC_7600/Rgu6spkG">CDC 7600</a>)</li></ul> <ul><li>16 bits: doublet,<a class="footnote-ref" id="fnref:45" href="#fn:45"><sup>45</sup></a> wyde,<a class="footnote-ref" id="fnref:46" href="#fn:46"><sup>46</sup></a><a class="footnote-ref" id="fnref:47" href="#fn:47"><sup>47</sup></a> parcel (on <a href="/facts/Cray-1/4afuzp0D">Cray-1</a>), chawmp (on a 32-bit machine)<a class="footnote-ref" id="fnref:48" href="#fn:48"><sup>48</sup></a></li></ul> <ul><li>18 bits: chomp, chawmp (on a 36-bit machine)<a class="footnote-ref" id="fnref:49" href="#fn:49"><sup>49</sup></a></li></ul> <ul><li>32 bits: quadlet,<a class="footnote-ref" id="fnref:50" href="#fn:50"><sup>50</sup></a><a class="footnote-ref" id="fnref:51" href="#fn:51"><sup>51</sup></a><a class="footnote-ref" id="fnref:52" href="#fn:52"><sup>52</sup></a> tetra<a class="footnote-ref" id="fnref:53" href="#fn:53"><sup>53</sup></a></li></ul> <ul><li>64 bits: octlet,<a class="footnote-ref" id="fnref:54" href="#fn:54"><sup>54</sup></a> octa<a class="footnote-ref" id="fnref:55" href="#fn:55"><sup>55</sup></a></li></ul> <ul><li>96 bits: bentobox (in <a href="/facts/ITRON_project/xE6dWQVQ">ITRON OS</a>)</li></ul> <ul><li>128 bits: hexlet,<a class="footnote-ref" id="fnref:56" href="#fn:56"><sup>56</sup></a><a class="footnote-ref" id="fnref:57" href="#fn:57"><sup>57</sup></a> <a href="/facts/Paragraph_(Intel)/7yD0VGfy">paragraph</a> (on <a href="/facts/Intel_x86/Kypq5fgu">Intel x86</a> processors)<a class="footnote-ref" id="fnref:58" href="#fn:58"><sup>58</sup></a><a class="footnote-ref" id="fnref:59" href="#fn:59"><sup>59</sup></a></li></ul> <ul><li>256 bytes: <a href="/facts/Page_(computer_memory)/CNGruG1H">page</a> (on Intel 4004,<a class="footnote-ref" id="fnref:60" href="#fn:60"><sup>60</sup></a> <a href="/facts/Intel_8080/32FvNTcD">8080</a> and 8086 processors,<a class="footnote-ref" id="fnref:61" href="#fn:61"><sup>61</sup></a> also many other 8-bit processors – typically much larger on many 16-bit/32-bit processors)</li></ul> <ul><li>6 trits: <a href="/facts/Tryte/bMUfR74P">tryte</a><a class="footnote-ref" id="fnref:62" href="#fn:62"><sup>62</sup></a></li></ul> <ul><li>combit, comword<a class="footnote-ref" id="fnref:63" href="#fn:63"><sup>63</sup></a><a class="footnote-ref" id="fnref:64" href="#fn:64"><sup>64</sup></a><a class="footnote-ref" id="fnref:65" href="#fn:65"><sup>65</sup></a></li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/File_size/nd3d84MN">File size</a></li> <li><a href="/facts/ISO_80000-13/k1nrIjMW">ISO 80000-13</a> (Quantities and units – Part 13: Information science and technology)</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="http://people.csail.mit.edu/jaffer/MIXF/MIXF-08">Representation of numerical values and SI units in character strings for information interchanges</a></li> <li><a href="http://www.bit-calculator.com">Bit Calculator</a> – Make conversions between bits, bytes, kilobits, kilobytes, megabits, megabytes, gigabits, gigabytes, terabits, terabytes, petabits, petabytes, exabits, exabytes, zettabits, zettabytes, yottabits, yottabytes.</li> <li><a href="http://www.cl.cam.ac.uk/~mgk25/information-units.txt">Paper on standardized units for use in information technology</a></li> <li><a href="https://www.gbmb.org/">Data Byte Converter</a></li> <li><a href="https://www.dataunitconverter.com/">High Precision Data Unit Converters</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Mackenzie, Charles E. (1980). Coded Character Sets, History and Development (PDF). The Systems Programming Series (1 ed.). Addison-Wesley Publishing Company, Inc. p. xii. ISBN 978-0-201-14460-4. LCCN 77-90165. Archived (PDF) from the original on May 26, 2016. Retrieved August 25, 2019. <a href="978-0-201-14460-4" target="_blank">978-0-201-14460-4</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Abramson, Norman (1963). Information theory and coding. McGraw-Hill. <a href="/wiki/McGraw-Hill" target="_blank">/wiki/McGraw-Hill</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Knuth, Donald Ervin. The Art of Computer Programming: Seminumerical algorithms. Vol. 2. Addison Wesley. <a href="/wiki/Donald_Ervin_Knuth" target="_blank">/wiki/Donald_Ervin_Knuth</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Abramson, Norman (1963). Information theory and coding. McGraw-Hill. <a href="/wiki/McGraw-Hill" target="_blank">/wiki/McGraw-Hill</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Shanmugam (2006). Digital and Analog Computer Systems. <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Jaeger, Gregg (2007). Quantum information: an overview. <a href="https://www.springer.com/physics/quantum+physics/book/978-0-387-35725-6" target="_blank">https://www.springer.com/physics/quantum+physics/book/978-0-387-35725-6</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Kumar, I. Ravi (2001). Comprehensive Statistical Theory of Communication. <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Abramson, Norman (1963). Information theory and coding. 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