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title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-定義" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#定義"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>定義</span> </div> </a> <ul id="toc-定義-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-與其他通用編碼的比較" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#與其他通用編碼的比較"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>與其他通用編碼的比較</span> </div> </a> <ul id="toc-與其他通用編碼的比較-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-例子" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#例子"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>例子</span> </div> </a> <ul id="toc-例子-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-斐波那契进制" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#斐波那契进制"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>斐波那契进制</span> </div> </a> <ul id="toc-斐波那契进制-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參見" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參見"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>參見</span> </div> </a> <ul id="toc-參見-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考资料" 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class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8%D0%B5%D0%B2%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%81%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F" title="Фибоначчиева система счисления – 俄语" lang="ru" hreflang="ru" data-title="Фибоначчиева система счисления" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F_%D0%A4%D1%96%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D1%96" title="Система числення Фібоначчі – 乌克兰语" lang="uk" hreflang="uk" data-title="Система числення Фібоначчі" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div 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src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></span></span></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><div id="noteTA-b9e12876" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Math"></div><div data-noteta-group-source="module" data-noteta-group="IT"></div></div><div class="noteTA-local"><div data-noteta-code="zh-tw:費波那契; zh-hk:費波那契; zh-cn:斐波那契;"></div></div></div> <p><b>斐波那契編碼</b>（Fibonacci coding）是一種僅使用兩種符號（0和1）表達數值的<span class="ilh-all" data-orig-title="通用編碼 (資料壓縮)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Universal code (data compression)"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%9A%E7%94%A8%E7%B7%A8%E7%A2%BC_(%E8%B3%87%E6%96%99%E5%A3%93%E7%B8%AE)&action=edit&redlink=1" class="new" title="通用編碼 (資料壓縮)（页面不存在）">通用編碼</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Universal_code_(data_compression)" class="extiw" title="en:Universal code (data compression)"><span lang="en" dir="auto">Universal code (data compression)</span></a></span>）</span></span><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。這種編碼是基於<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8" class="mw-redirect" title="斐波那契數">斐波那契數</a>來表達整數的一個例子。這種編碼皆以「11」為結尾，並且在結尾之前不會出現連續2個1。 </p><p>斐波那契編碼與<a href="/wiki/%E9%BD%8A%E8%82%AF%E5%A4%9A%E5%A4%AB%E5%AE%9A%E7%90%86" title="齊肯多夫定理">齊肯多夫表述法</a>密切相關。齊肯多夫表述法是一種基於<a href="/wiki/%E9%BD%8A%E8%82%AF%E5%A4%9A%E5%A4%AB%E5%AE%9A%E7%90%86" title="齊肯多夫定理">齊肯多夫定理</a>的进制系統，並且也具有不連續使用兩個1的特性。特定整數的斐波那契編碼正是數字順序顛倒的齊肯多夫表述法，並在末尾附加了一個額外的“1”。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="定義"><span id=".E5.AE.9A.E7.BE.A9"></span>定義</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&action=edit&section=1" title="编辑章节：定義"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>對於一個數字<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4df206628eed61b48a8c51b432eca0c6520179e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N\!}"></span>，若<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d(0),d(1),\ldots ,d(k-1),d(k)\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mi>d</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>d</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mi>d</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d(0),d(1),\ldots ,d(k-1),d(k)\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/262078eeffcf8661bf8168002c1ff818e2d9b2f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:27.876ex; height:2.843ex;" alt="{\displaystyle d(0),d(1),\ldots ,d(k-1),d(k)\!}"></span>代表<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4df206628eed61b48a8c51b432eca0c6520179e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N\!}"></span>在斐波那契編碼中的<span class="ilh-all" data-orig-title="碼字" data-lang-code="en" data-lang-name="英语" data-foreign-title="code word"><span class="ilh-page"><a href="/w/index.php?title=%E7%A2%BC%E5%AD%97&action=edit&redlink=1" class="new" title="碼字（页面不存在）">碼字</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/code_word" class="extiw" title="en:code word"><span lang="en" dir="auto">code word</span></a></span>）</span></span>，則有： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=\sum _{i=0}^{k-1}d(i)F(i+2),{\text{ and }}d(k-1)=d(k)=1.\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <mi>d</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> and </mtext> </mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>d</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1.</mn> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=\sum _{i=0}^{k-1}d(i)F(i+2),{\text{ and }}d(k-1)=d(k)=1.\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53b83695d56b770fb163ba478fa2f9d9aa2c6a52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.204ex; width:47.328ex; height:7.343ex;" alt="{\displaystyle N=\sum _{i=0}^{k-1}d(i)F(i+2),{\text{ and }}d(k-1)=d(k)=1.\!}"></span></dd></dl> <p>其中<style data-mw-deduplicate="TemplateStyles:r58896141">.mw-parser-output .serif{font-family:Times,serif}</style><span class="serif"><span class="texhtml"><i>F</i>(<i>i</i>)</span></span>為第<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>i</i></span></span>個<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8" class="mw-redirect" title="斐波那契數">斐波那契數</a>，因此<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>F</i>(<i>i</i>+2)</span></span>是第<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>i</i></span></span>個相異的<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8" class="mw-redirect" title="斐波那契數">斐波那契數</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1,2,3,5,8,13,\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>8</mn> <mo>,</mo> <mn>13</mn> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1,2,3,5,8,13,\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a65971693987807896a13cbf12a1398b8c0a02d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.064ex; height:2.509ex;" alt="{\displaystyle 1,2,3,5,8,13,\ldots }"></span>。最後一位<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d(k)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d(k)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b59ae56ed5fb312c7303526a49d562e31ea20909" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.236ex; height:2.843ex;" alt="{\displaystyle d(k)}"></span>為始終是1的附加位，並且不攜帶位置值。 </p><p>可以看出，這樣的編碼是唯一的，並且在任何碼字中唯一出現的“11”是在末尾，即<i>d</i>(<i>k</i>−1)和<i>d</i>(<i>k</i>)。倒數第二位是最高有效位，第一位是最低有效位。許多进制可以省略前導零，如十进制，然而斐波那契編碼的前導零不能省略。 </p><p>下面顯示了前幾個斐波那契編碼，以及其所謂的隱含概率，即對所有在斐波那契編碼中有最小碼值的數字而言的值。 </p> <table class="wikitable" style="text-align:right;"> <tbody><tr> <th>數字</th> <th>斐波那契表述法</th> <th>斐波那契編碼</th> <th>隱含概率 </th></tr> <tr> <td>1</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96ed3f1c8861a0fd967b693342b1692c01ea25c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.713ex; height:2.843ex;" alt="{\displaystyle F(2)}"></span></td> <td>11</td> <td>1/4 </td></tr> <tr> <td>2</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f41ad9360c4645b946b1c9915aaf6f0e35eed65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.713ex; height:2.843ex;" alt="{\displaystyle F(3)}"></span></td> <td>011</td> <td>1/8 </td></tr> <tr> <td>3</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(4)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(4)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6072d779036bf7be20a086c085530915be02ccf5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.713ex; height:2.843ex;" alt="{\displaystyle F(4)}"></span></td> <td>0011</td> <td>1/16 </td></tr> <tr> <td>4</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(2)+F(4)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(2)+F(4)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4412431306d06aaa6c04fb46a1ca4140a5c3221" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.265ex; height:2.843ex;" alt="{\displaystyle F(2)+F(4)}"></span></td> <td>1011</td> <td>1/16 </td></tr> <tr> <td>5</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(5)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(5)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa1d5dff0c4bffae5648b2c75b28599ac5956c35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.713ex; height:2.843ex;" alt="{\displaystyle F(5)}"></span></td> <td>00011</td> <td>1/32 </td></tr> <tr> <td>6</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(2)+F(5)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(2)+F(5)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e934370caaff4714ca611c7a325677d9457c4251" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.265ex; height:2.843ex;" alt="{\displaystyle F(2)+F(5)}"></span></td> <td>10011</td> <td>1/32 </td></tr> <tr> <td>7</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(3)+F(5)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(3)+F(5)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0df76cdbd737392b71a620751996c8aa036a6b34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.265ex; height:2.843ex;" alt="{\displaystyle F(3)+F(5)}"></span></td> <td>01011</td> <td>1/32 </td></tr> <tr> <td>8</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/983c1d8e6d1d9c192089bdfc38b252082c45413f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.713ex; height:2.843ex;" alt="{\displaystyle F(6)}"></span></td> <td>000011</td> <td>1/64 </td></tr> <tr> <td>9</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(2)+F(6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(2)+F(6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e8c616d0596bee0b623fb517e3520f58b39f3bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.265ex; height:2.843ex;" alt="{\displaystyle F(2)+F(6)}"></span></td> <td>100011</td> <td>1/64 </td></tr> <tr> <td>10</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(3)+F(6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(3)+F(6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df2d4bb9ae6e432e432b1d08c2b5ac072d4c3009" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.265ex; height:2.843ex;" alt="{\displaystyle F(3)+F(6)}"></span></td> <td>010011</td> <td>1/64 </td></tr> <tr> <td>11</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(4)+F(6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(4)+F(6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4df6067228dd0211dd7a8669fbd2b2c03998c7a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.265ex; height:2.843ex;" alt="{\displaystyle F(4)+F(6)}"></span></td> <td>001011</td> <td>1/64 </td></tr> <tr> <td>12</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(2)+F(4)+F(6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(2)+F(4)+F(6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5912de446a9f25cbfe4d6e106eb4ab95d1987290" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.818ex; height:2.843ex;" alt="{\displaystyle F(2)+F(4)+F(6)}"></span></td> <td>101011</td> <td>1/64 </td></tr> <tr> <td>13</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(7)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(7)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21f23316637ae7b32258efcc5e6f305938df973f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.713ex; height:2.843ex;" alt="{\displaystyle F(7)}"></span></td> <td>0000011</td> <td>1/128 </td></tr> <tr> <td>14</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(2)+F(7)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(2)+F(7)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8402b6e67fdd68c639b259ce405114665eda6642" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.265ex; height:2.843ex;" alt="{\displaystyle F(2)+F(7)}"></span></td> <td>1000011</td> <td>1/128 </td></tr> </tbody></table> <p>將一個整數N編碼為斐波那契編碼的方法為： </p> <ol><li>找到小於或等於<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>N</i></span></span>的最大<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8" class="mw-redirect" title="斐波那契數">斐波那契數</a>，並且用<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>N</i></span></span>減去這個<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8" class="mw-redirect" title="斐波那契數">斐波那契數</a>，並記錄剩餘的數</li> <li>如果減去的這個數為為第<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>i</i></span></span>個<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8" class="mw-redirect" title="斐波那契數">斐波那契數</a><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>F</i>(<i>i</i>)</span></span>，置1到<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>i</i>−2</span></span>的位置（將最左邊的數字視為位置0）。</li> <li>將<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>N</i></span></span>替換為剩餘的數，並重複步驟1~2直到剩餘的數為0</li> <li>在最右邊加一個「1」</li></ol> <p>要解碼斐波那契編碼，請刪除最後的「1」，將剩餘的位數分配給1,2,3,5,8,13...（斐波那契數），並將位數為「1」的斐波那契數加總。 </p> <div class="mw-heading mw-heading2"><h2 id="與其他通用編碼的比較"><span id=".E8.88.87.E5.85.B6.E4.BB.96.E9.80.9A.E7.94.A8.E7.B7.A8.E7.A2.BC.E7.9A.84.E6.AF.94.E8.BC.83"></span>與其他通用編碼的比較</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&action=edit&section=2" title="编辑章节：與其他通用編碼的比較"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>斐波那契編碼有一個有用的特性，有時它與其他<span class="ilh-all" data-orig-title="通用編碼 (資料壓縮)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Universal code (data compression)"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%9A%E7%94%A8%E7%B7%A8%E7%A2%BC_(%E8%B3%87%E6%96%99%E5%A3%93%E7%B8%AE)&action=edit&redlink=1" class="new" title="通用編碼 (資料壓縮)（页面不存在）">通用編碼</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Universal_code_(data_compression)" class="extiw" title="en:Universal code (data compression)"><span lang="en" dir="auto">Universal code (data compression)</span></a></span>）</span></span>相比更具吸引力：斐波那契編碼是<span class="ilh-all" data-orig-title="自同步編碼" data-lang-code="en" data-lang-name="英语" data-foreign-title="Self-synchronizing code"><span class="ilh-page"><a href="/w/index.php?title=%E8%87%AA%E5%90%8C%E6%AD%A5%E7%B7%A8%E7%A2%BC&action=edit&redlink=1" class="new" title="自同步編碼（页面不存在）">自同步編碼</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Self-synchronizing_code" class="extiw" title="en:Self-synchronizing code"><span lang="en" dir="auto">Self-synchronizing code</span></a></span>）</span></span>的一個示例，可以更容易地從損壞的<a href="/wiki/%E8%B3%87%E6%96%99%E6%B5%81" title="資料流">資料流</a>中恢復數據。對於大多數其他<span class="ilh-all" data-orig-title="通用編碼 (資料壓縮)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Universal code (data compression)"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%9A%E7%94%A8%E7%B7%A8%E7%A2%BC_(%E8%B3%87%E6%96%99%E5%A3%93%E7%B8%AE)&action=edit&redlink=1" class="new" title="通用編碼 (資料壓縮)（页面不存在）">通用編碼</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Universal_code_(data_compression)" class="extiw" title="en:Universal code (data compression)"><span lang="en" dir="auto">Universal code (data compression)</span></a></span>）</span></span>，如果單個<a href="/wiki/%E4%BD%8D%E5%85%83" title="位元">位元</a>被更改，則其後的任何數據可能無法被正確讀取。另一方面，對於斐波那契編碼，更改位元可能會導致一個字詞（token）被讀取為兩個，或者導致兩個字詞被錯誤地讀取為一個，但從資料流中讀取“0”能阻止錯誤進一步傳播。由於唯一沒有“0”的資料流是“11”字詞的資料流，因此單個位元錯誤損壞的資料流與原始資料流之間的總<a href="/wiki/%E7%B7%A8%E8%BC%AF%E8%B7%9D%E9%9B%A2" title="編輯距離">編輯距離</a>最多為3。 </p><p>在這種使用符號序列進行編碼的方法中，可以自由推廣其中某些不允許存在的模式（如“11”）。<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="例子"><span id=".E4.BE.8B.E5.AD.90"></span>例子</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&action=edit&section=3" title="编辑章节：例子"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>下表展示了整數65編碼到斐波那契编码為0100100011的具體內容，表示<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 65={{{2}+{8}}+{55}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>65</mn> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>55</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 65={{{2}+{8}}+{55}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/940d11daa4f707a4b11e0bab33f359fa8d414416" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.754ex; height:2.343ex;" alt="{\displaystyle 65={{{2}+{8}}+{55}}}"></span>。不使用前兩個斐波那契數<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>F</i>(0)=0</span></span>和<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml"><i>F</i>(1)=1</span></span>，且末尾必定會加上一個「1」。 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{ccccccccccc|c}\hline 0&1&1&2&3&5&8&13&21&34&55&-\\\hline F(0)&F(1)&F(2)&F(3)&F(4)&F(5)&F(6)&F(7)&F(8)&F(9)&F(10)&\scriptstyle {\text{additional}}\\\hline -&-&0&1&0&0&1&0&0&0&1&1\\\hline \end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <menclose notation="top bottom"> <mtable columnalign="center center center center center center center center center center center center" rowspacing="4pt" columnspacing="1em" rowlines="solid solid" columnlines="none none none none none none none none none none solid"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>13</mn> </mtd> <mtd> <mn>21</mn> </mtd> <mtd> <mn>34</mn> </mtd> <mtd> <mn>55</mn> </mtd> <mtd> <mo>−</mo> </mtd> </mtr> <mtr> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>8</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>9</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mn>10</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>additional</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> </mtd> <mtd> <mo>−</mo> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </menclose> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{ccccccccccc|c}\hline 0&1&1&2&3&5&8&13&21&34&55&-\\\hline F(0)&F(1)&F(2)&F(3)&F(4)&F(5)&F(6)&F(7)&F(8)&F(9)&F(10)&\scriptstyle {\text{additional}}\\\hline -&-&0&1&0&0&1&0&0&0&1&1\\\hline \end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e39fad4dcdf757d0df2d0cbdf1e71f4082dcb992" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.838ex; width:87.951ex; height:10.843ex;" alt="{\displaystyle {\begin{array}{ccccccccccc|c}\hline 0&1&1&2&3&5&8&13&21&34&55&-\\\hline F(0)&F(1)&F(2)&F(3)&F(4)&F(5)&F(6)&F(7)&F(8)&F(9)&F(10)&\scriptstyle {\text{additional}}\\\hline -&-&0&1&0&0&1&0&0&0&1&1\\\hline \end{array}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="斐波那契进制"><span id=".E6.96.90.E6.B3.A2.E9.82.A3.E5.A5.91.E8.BF.9B.E5.88.B6"></span>斐波那契进制</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&action=edit&section=4" title="编辑章节：斐波那契进制"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>斐波那契进制</b>（Fibonaccimal Base）是與<a href="/wiki/%E9%BB%84%E9%87%91%E8%BF%9B%E5%88%B6" title="黄金进制">黃金进制</a>關係緊密的計數系統。它只用0和1表示數，每個數位的位值對應<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8" class="mw-redirect" title="斐波那契數">斐波那契數</a><sup id="cite_ref-Fibonaccimal_Base_3-0" class="reference"><a href="#cite_note-Fibonaccimal_Base-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>。和黃金进制一樣，其標準形也不連續使用兩個1。如： </p> <dl><dd><dl><dd>30 = 1×21 + 0×13 + 1×8 + 0×5 + 0×3 + 0×2 + 1×1 + 0×1 = 10100010<sub>fib</sub></dd></dl></dd></dl> <p>斐波那契进制與<a href="/wiki/%E9%BD%8A%E8%82%AF%E5%A4%9A%E5%A4%AB%E5%AE%9A%E7%90%86" title="齊肯多夫定理">齊肯多夫表述法</a>非常接近，斐波那契进制僅比齊肯多夫表述法末尾附加了一個額外的“0”。 </p><p>由於最末位始終為零，因此有時會將之省去<sup id="cite_ref-Fibonaccimal_Base_3-1" class="reference"><a href="#cite_note-Fibonaccimal_Base-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>，而省去後的結果則與<a href="/wiki/%E9%BD%8A%E8%82%AF%E5%A4%9A%E5%A4%AB%E5%AE%9A%E7%90%86" title="齊肯多夫定理">齊肯多夫表述法</a>相同<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="參見"><span id=".E5.8F.83.E8.A6.8B"></span>參見</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&action=edit&section=5" title="编辑章节：參見"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E9%80%B2%E4%BD%8D%E5%88%B6" class="mw-redirect" title="進位制">進位制</a></li> <li><a href="/wiki/%E9%BB%84%E9%87%91%E8%BF%9B%E5%88%B6" title="黄金进制">黃金進制</a></li> <li><span class="ilh-all" data-orig-title="负斐波那契编码" data-lang-code="en" data-lang-name="英语" data-foreign-title="Negafibonacci coding"><span class="ilh-page"><a href="/w/index.php?title=%E8%B4%9F%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&action=edit&redlink=1" class="new" title="负斐波那契编码（页面不存在）">负斐波那契编码</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Negafibonacci_coding" class="extiw" title="en:Negafibonacci coding"><span lang="en" dir="auto">Negafibonacci coding</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="奧斯特洛夫斯基记数系统" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ostrowski numeration"><span class="ilh-page"><a href="/w/index.php?title=%E5%A5%A7%E6%96%AF%E7%89%B9%E6%B4%9B%E5%A4%AB%E6%96%AF%E5%9F%BA%E8%AE%B0%E6%95%B0%E7%B3%BB%E7%BB%9F&action=edit&redlink=1" class="new" title="奧斯特洛夫斯基记数系统（页面不存在）">奧斯特洛夫斯基记数系统</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ostrowski_numeration" class="extiw" title="en:Ostrowski numeration"><span lang="en" dir="auto">Ostrowski numeration</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="通用編碼 (資料壓縮)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Universal code (data compression)"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%9A%E7%94%A8%E7%B7%A8%E7%A2%BC_(%E8%B3%87%E6%96%99%E5%A3%93%E7%B8%AE)&action=edit&redlink=1" class="new" title="通用編碼 (資料壓縮)（页面不存在）">通用編碼</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Universal_code_(data_compression)" class="extiw" title="en:Universal code (data compression)"><span lang="en" dir="auto">Universal code (data compression)</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%BD%8A%E8%82%AF%E5%A4%9A%E5%A4%AB%E5%AE%9A%E7%90%86" title="齊肯多夫定理">齊肯多夫定理</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="参考资料"><span id=".E5.8F.82.E8.80.83.E8.B5.84.E6.96.99"></span>参考资料</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&action=edit&section=6" title="编辑章节：参考资料"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r80540462">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .refbegin-100{font-size:100%}</style><div class="refbegin" style=""> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation journal">Ayse Nalli, Cagla Ozyilmaz. <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0022314X14002492">The third order variations on the Fibonacci universal code</a>. Journal of Number Theory. 2015-04, <b>149</b>: 15–32 <span class="reference-accessdate"> [<span class="nowrap">2022-10-06</span>]</span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jnt.2014.07.010"><span title="數位物件識別號">doi:10.1016/j.jnt.2014.07.010</span></a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20180629180708/https://linkinghub.elsevier.com/retrieve/pii/S0022314X14002492">存档</a>于2018-06-29） <span style="font-family: sans-serif; cursor: default; color:var(--color-subtle, #54595d); font-size: 0.8em; bottom: 0.1em; font-weight: bold;" title="连接到英语网页">（英语）</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&rft.atitle=The+third+order+variations+on+the+Fibonacci+universal+code&rft.au=Ayse+Nalli%2C+Cagla+Ozyilmaz&rft.date=2015-04&rft.genre=article&rft.jtitle=Journal+of+Number+Theory&rft.pages=15-32&rft.volume=149&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0022314X14002492&rft_id=info%3Adoi%2F10.1016%2Fj.jnt.2014.07.010&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation arxiv">Duda, Jarek. Optimal encoding on discrete lattice with translational invariant constrains using statistical algorithms. 2007. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/0710.3861"><span title="arXiv">arXiv:0710.3861</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span> [<a rel="nofollow" class="external text" href="//arxiv.org/archive/cs.IT">cs.IT</a>].</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&rft.atitle=Optimal+encoding+on+discrete+lattice+with+translational+invariant+constrains+using+statistical+algorithms&rft.aufirst=Jarek&rft.aulast=Duda&rft.date=2007&rft.genre=preprint&rft.jtitle=arXiv&rft_id=info%3Aarxiv%2F0710.3861&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Fibonaccimal_Base-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Fibonaccimal_Base_3-0"><sup><b>3.0</b></sup></a> <a href="#cite_ref-Fibonaccimal_Base_3-1"><sup><b>3.1</b></sup></a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=889">Fibonaccimal Base</a>. onlinejudge.org. <span class="reference-accessdate"> [<span class="nowrap">2022-10-06</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20221009151415/https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=889">存档</a>于2022-10-09）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&rft.atitle=Fibonaccimal+Base&rft.genre=unknown&rft.jtitle=onlinejudge.org&rft_id=https%3A%2F%2Fonlinejudge.org%2Findex.php%3Foption%3Dcom_onlinejudge%26Itemid%3D8%26category%3D24%26page%3Dshow_problem%26problem%3D889&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite class="citation web"><a href="/wiki/Neil_Sloane" class="mw-redirect" title="Neil Sloane">Sloane, N.J.A.</a> (编). <a rel="nofollow" class="external text" href="https://oeis.org/A014417">Sequence A014417 (Representation of n in base of Fibonacci numbers (the Zeckendorf representation of n))</a>. The <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" class="mw-redirect" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a>. OEIS Foundation.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&rft.atitle=Sequence%26%23x20%3BA014417%26%23x20%3B%28Representation+of+n+in+base+of+Fibonacci+numbers+%28the+Zeckendorf+representation+of+n%29%29&rft.aufirst=N.J.A.&rft.aulast=Sloane&rft.genre=unknown&rft.jtitle=The+On-Line+Encyclopedia+of+Integer+Sequences&rft_id=https%3A%2F%2Foeis.org%2FA014417&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <ul><li><cite class="citation book">Allouche, Jean-Paul; <a href="/w/index.php?title=Jeffrey_Shallit&action=edit&redlink=1" class="new" title="Jeffrey Shallit（页面不存在）">Shallit, Jeffrey</a>. <a rel="nofollow" class="external text" href="https://archive.org/details/automaticsequenc00jpal">Automatic Sequences: Theory, Applications, Generalizations</a><span typeof="mw:File"><span title="有限度免费查阅，超限则需付费订阅"><img alt="有限度免费查阅，超限则需付费订阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lock-blue-alt-2.svg/9px-Lock-blue-alt-2.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lock-blue-alt-2.svg/14px-Lock-blue-alt-2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lock-blue-alt-2.svg/18px-Lock-blue-alt-2.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span>. <a href="/wiki/Cambridge_University_Press" class="mw-redirect" title="Cambridge University Press">Cambridge University Press</a>. 2003: <a rel="nofollow" class="external text" href="https://archive.org/details/automaticsequenc00jpal/page/n122">105</a>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-521-82332-6" title="Special:网络书源/978-0-521-82332-6"><span title="国际标准书号">ISBN</span> 978-0-521-82332-6</a>. <a rel="nofollow" class="external text" href="//zbmath.org/?format=complete&q=an:1086.11015"><span title="Zentralblatt MATH">Zbl 1086.11015</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&rft.au=Shallit%2C+Jeffrey&rft.aufirst=Jean-Paul&rft.aulast=Allouche&rft.btitle=Automatic+Sequences%3A+Theory%2C+Applications%2C+Generalizations&rft.date=2003&rft.genre=book&rft.isbn=978-0-521-82332-6&rft.pages=105&rft.pub=Cambridge+University+Press&rft_id=%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A1086.11015&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fautomaticsequenc00jpal&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation journal">Fraenkel, Aviezri S.; Klein, Shmuel T. Robust universal complete codes for transmission and compression. Discrete Applied Mathematics. 1996, <b>64</b> (1): 31–55. <span class="plainlinks"><a rel="nofollow" class="external text" href="//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.3064"><span title="CiteSeerX">CiteSeerX 10.1.1.37.3064</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0166-218X"><span title="国际标准连续出版物号">ISSN 0166-218X</span></a>. <a rel="nofollow" class="external text" href="//zbmath.org/?format=complete&q=an:0874.94026"><span title="Zentralblatt MATH">Zbl 0874.94026</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0166-218X%2893%2900116-H"><span title="數位物件識別號">doi:10.1016/0166-218X(93)00116-H</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81&rft.atitle=Robust+universal+complete+codes+for+transmission+and+compression&rft.au=Klein%2C+Shmuel+T.&rft.aufirst=Aviezri+S.&rft.aulast=Fraenkel&rft.date=1996&rft.genre=article&rft.issn=0166-218X&rft.issue=1&rft.jtitle=Discrete+Applied+Mathematics&rft.pages=31-55&rft.volume=64&rft_id=%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.37.3064&rft_id=%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A0874.94026&rft_id=info%3Adoi%2F10.1016%2F0166-218X%2893%2900116-H&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li></ul> </div> <p class="mw-empty-elt"> </p> <div 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class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%B8%80%E8%BF%9B%E5%88%B6" title="一进制">一进制</a></li> <li><a href="/wiki/%E4%BA%8C%E8%BF%9B%E5%88%B6" title="二进制">二进制</a></li> <li><a href="/wiki/%E4%B8%89%E8%BF%9B%E5%88%B6" title="三进制">三进制</a></li> <li><a href="/wiki/%E5%9B%9B%E9%80%B2%E5%88%B6" title="四進制">四进制</a></li> <li><a href="/wiki/%E4%BA%94%E9%80%B2%E5%88%B6" title="五進制">五进制</a></li> <li><a href="/wiki/%E5%85%AD%E8%BF%9B%E5%88%B6" title="六进制">六进制</a></li> <li><a href="/w/index.php?title=%E4%B8%83%E9%80%B2%E5%88%B6&action=edit&redlink=1" class="new" title="七進制（页面不存在）">七進制</a></li> <li><a href="/wiki/%E5%85%AB%E8%BF%9B%E5%88%B6" title="八进制">八进制</a></li> <li><a href="/wiki/%E4%B9%9D%E9%80%B2%E4%BD%8D" title="九進位">九进制</a></li> <li><a href="/wiki/%E5%8D%81%E8%BF%9B%E5%88%B6" title="十进制">十进制</a></li> <li><a href="/wiki/%E5%8D%81%E4%B8%80%E8%BF%9B%E5%88%B6" title="十一进制">十一进制</a></li> <li><a href="/wiki/%E5%8D%81%E4%BA%8C%E8%BF%9B%E5%88%B6" title="十二进制">十二进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%B8%89%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="十三进制（页面不存在）">十三进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E5%9B%9B%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="十四进制（页面不存在）">十四进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%BA%94%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="十五进制（页面不存在）">十五进制</a></li> <li><a href="/wiki/%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" title="十六进制">十六进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%B8%83%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="十七进制（页面不存在）">十七进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E5%85%AB%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="十八进制（页面不存在）">十八进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%B9%9D%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="十九进制（页面不存在）">十九进制</a></li> <li><a href="/wiki/%E4%BA%8C%E5%8D%81%E8%BF%9B%E5%88%B6" title="二十进制">二十进制</a></li> <li><a href="/wiki/%E4%BA%8C%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" class="mw-disambig" title="二十六进制">二十六进制</a></li> <li><a href="/wiki/%E4%B8%89%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" title="三十六进制">三十六进制</a></li> <li><a href="/wiki/%E5%85%AD%E5%8D%81%E9%80%B2%E5%88%B6" title="六十進制">六十进制</a></li> <li><a href="/wiki/%E8%BF%9B%E4%BD%8D%E5%88%B6" title="进位制">六十四进制</a></li> <li><a href="/w/index.php?title=%E4%B8%80%E7%99%BE%E9%80%B2%E5%88%B6&action=edit&redlink=1" class="new" title="一百進制（页面不存在）">一百进制</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">平衡进位制</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%B9%B3%E8%A1%A1%E4%B8%89%E9%80%B2%E4%BD%8D" title="平衡三進位">平衡三进制</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%B9%BF%E4%B9%89%E7%9A%84%E8%BF%9B%E5%88%B6%E7%B3%BB%E7%BB%9F" title="广义的进制系统">广义的进制系统</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Base64" title="Base64">Base64</a></li> <li><a href="/wiki/%E5%8D%81%E8%BF%9B%E5%88%B6#十进位制" title="十进制">十进位制</a></li> <li><a href="/w/index.php?title=%E4%BA%8C%E9%80%B2%E6%8C%87%E6%95%B8%E6%B3%95&action=edit&redlink=1" class="new" title="二進指數法（页面不存在）">二進指數法</a></li> <li><a href="/wiki/%E9%9D%9E%E6%95%B4%E6%95%B0%E8%BF%9B%E4%BD%8D%E5%88%B6" title="非整数进位制">非整数进位制</a> <ul><li><a href="/w/index.php?title=%E6%A0%B9%E5%8F%B72%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="根号2进制（页面不存在）">根號2进制</a></li> <li><a href="/wiki/%E9%BB%84%E9%87%91%E8%BF%9B%E5%88%B6" title="黄金进制">黄金进制</a></li> <li><a href="/wiki/E%E8%BF%9B%E5%88%B6" title="E进制">e进制</a></li></ul></li> <li><span class="ilh-all" data-orig-title="负底数进制" data-lang-code="en" data-lang-name="英语" data-foreign-title="Negative base"><span class="ilh-page"><a href="/w/index.php?title=%E8%B4%9F%E5%BA%95%E6%95%B0%E8%BF%9B%E5%88%B6&action=edit&redlink=1" class="new" title="负底数进制（页面不存在）">负底数进制</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Negative_base" class="extiw" title="en:Negative base"><span lang="en" dir="auto">Negative base</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%A4%8D%E5%BA%95%E6%95%B0%E8%BF%9B%E5%88%B6" title="复底数进制">複底数进制</a> <ul><li><a href="/wiki/2i%E9%80%B2%E5%88%B6" title="2i進制">2i进制</a></li> <li><a href="/wiki/-1%C2%B1i%E8%BF%9B%E5%88%B6" class="mw-redirect" title="-1±i进制">-1±i进制</a></li></ul></li> <li><span class="ilh-all" data-orig-title="混合底數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mixed radix"><span class="ilh-page"><a href="/w/index.php?title=%E6%B7%B7%E5%90%88%E5%BA%95%E6%95%B8&action=edit&redlink=1" class="new" title="混合底數（页面不存在）">混合底數</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mixed_radix" class="extiw" title="en:Mixed radix"><span lang="en" dir="auto">Mixed radix</span></a></span>）</span></span> <ul><li><a href="/wiki/%E9%98%B6%E4%B9%98%E8%BF%9B%E5%88%B6" title="阶乘进制">阶乘进制</a></li></ul></li> <li><a class="mw-selflink selflink">斐波那契編碼</a></li> <li><a href="/wiki/%E9%9B%99%E5%B0%84%E8%A8%98%E6%95%B8" title="雙射記數">双射记数系统</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">相關條目</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BA%95%E6%95%B0_(%E8%BF%9B%E5%88%B6)" title="底数 (进制)">底数</a></li> <li><a href="/wiki/%E6%95%B0%E4%BD%8D_(%E6%95%B0%E5%AD%A6)" title="数位 (数学)">数位</a></li> <li><a href="/wiki/%E4%BD%8D%E5%85%83" title="位元"> 比特 </a></li> <li><a href="/wiki/%E5%AD%97%E8%8A%82" title="字节">位元組</a></li> <li><a href="/wiki/%E8%BF%9B%E4%BD%8D%E5%88%B6" title="进位制">进位制</a></li> <li><a href="/wiki/%E7%B1%B3%E8%BF%AA%E5%AE%9A%E7%90%86" title="米迪定理">米迪定理</a></li> <li><a href="/wiki/%E8%AE%B0%E6%95%B0%E7%B3%BB%E7%BB%9F" title="记数系统">记数系统</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=斐波那契编码&oldid=80498987">https://zh.wikipedia.org/w/index.php?title=斐波那契编码&oldid=80498987</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" 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