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<title>Base64</title>
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<wx:section level="1" title="Base64" id="wxsec1"><h1 class="pagetitle" id="wx1">Base64</h1>

<p id="wx2"><b id="wx3">Base64</b> è un <a href="/wit/Sistema_di_numerazione" title="Sistema di numerazione" wx:linktype="known" wx:pagename="Sistema_di_numerazione" wx:page_id="17424" id="wx4">sistema di numerazione</a> posizionale che usa 64 simboli.</p>

<p id="wx5">Viene usato principalmente come codifica di dati binari nelle <a href="/wit/E-mail" title="E-mail" wx:linktype="known" wx:pagename="E-mail" wx:page_id="1664" id="wx6">e-mail</a>, per convertire i dati nel formato <a href="/wit/ASCII" title="ASCII" wx:linktype="known" wx:pagename="ASCII" wx:page_id="595" id="wx7">ASCII</a>.</p>

<a id="L.27algoritmo" name="L.27algoritmo"/>
<wx:section level="2" title="L'algoritmo" id="wxsec2"><h2 id="wx8">L'algoritmo</h2>

<p id="wx9">L'<a href="/wit/Algoritmo" title="Algoritmo" wx:linktype="known" wx:pagename="Algoritmo" wx:page_id="16" id="wx10">algoritmo</a> che effettua la conversione suddivide il file in gruppi da 6 <a href="/wit/Bit" title="Bit" wx:linktype="known" wx:pagename="Bit" wx:page_id="82006" id="wx11">bit</a>, i quali possono quindi contenere valori da 0 a 63. Ogni possibile valore viene convertito in un carattere <a href="/wit/ASCII" title="ASCII" wx:linktype="known" wx:pagename="ASCII" wx:page_id="595" id="wx12">ASCII</a> secondo la seguente tabella:</p>

<wx:template id="wx_t1" pagename="Template:MultiCol" page_id="653968"/>
<div id="wx13">
<table width="100%" border="0" cellspacing="0" cellpadding="0" style="background-color:transparent; table-layout:fixed" id="wx14">
<tr valign="top" id="wx15">
<td id="wx16">
<div style="margin-right:20px" id="wx17"><wx:templateend start="wx_t1"/>
<table border="1" cellpadding="3" cellspacing="0" id="wx18">
<tr id="wx19">
<th id="wx20">
<p id="wx21">Valore</p>
</th>
<th id="wx22">
<p id="wx23">ASCII</p>
</th>
</tr>

<tr id="wx24">
<td align="center" id="wx25">
<p id="wx26">0</p>
</td>
<td align="center" id="wx27"><tt id="wx28">A</tt> </td>
</tr>

<tr id="wx29">
<td align="center" id="wx30">
<p id="wx31">1</p>
</td>
<td align="center" id="wx32"><tt id="wx33">B</tt> </td>
</tr>

<tr id="wx34">
<td align="center" id="wx35">
<p id="wx36">2</p>
</td>
<td align="center" id="wx37"><tt id="wx38">C</tt> </td>
</tr>

<tr id="wx39">
<td align="center" id="wx40">
<p id="wx41">3</p>
</td>
<td align="center" id="wx42"><tt id="wx43">D</tt> </td>
</tr>

<tr id="wx44">
<td align="center" id="wx45">
<p id="wx46">4</p>
</td>
<td align="center" id="wx47"><tt id="wx48">E</tt> </td>
</tr>

<tr id="wx49">
<td align="center" id="wx50">
<p id="wx51">5</p>
</td>
<td align="center" id="wx52"><tt id="wx53">F</tt> </td>
</tr>

<tr id="wx54">
<td align="center" id="wx55">
<p id="wx56">6</p>
</td>
<td align="center" id="wx57"><tt id="wx58">G</tt> </td>
</tr>

<tr id="wx59">
<td align="center" id="wx60">
<p id="wx61">7</p>
</td>
<td align="center" id="wx62"><tt id="wx63">H</tt> </td>
</tr>

<tr id="wx64">
<td align="center" id="wx65">
<p id="wx66">8</p>
</td>
<td align="center" id="wx67"><tt id="wx68">I</tt> </td>
</tr>

<tr id="wx69">
<td align="center" id="wx70">
<p id="wx71">9</p>
</td>
<td align="center" id="wx72"><tt id="wx73">J</tt> </td>
</tr>

<tr id="wx74">
<td align="center" id="wx75">
<p id="wx76">10</p>
</td>
<td align="center" id="wx77"><tt id="wx78">K</tt> </td>
</tr>

<tr id="wx79">
<td align="center" id="wx80">
<p id="wx81">11</p>
</td>
<td align="center" id="wx82"><tt id="wx83">L</tt> </td>
</tr>

<tr id="wx84">
<td align="center" id="wx85">
<p id="wx86">12</p>
</td>
<td align="center" id="wx87"><tt id="wx88">M</tt> </td>
</tr>

<tr id="wx89">
<td align="center" id="wx90">
<p id="wx91">13</p>
</td>
<td align="center" id="wx92"><tt id="wx93">N</tt> </td>
</tr>

<tr id="wx94">
<td align="center" id="wx95">
<p id="wx96">14</p>
</td>
<td align="center" id="wx97"><tt id="wx98">O</tt> </td>
</tr>

<tr id="wx99">
<td align="center" id="wx100">
<p id="wx101">15</p>
</td>
<td align="center" id="wx102"><tt id="wx103">P</tt> </td>
</tr>
</table>

<wx:template id="wx_t2" pagename="Template:ColBreak" page_id="653969"/>
</div>
</td>
<td id="wx104">
<div style="margin-right:20px" id="wx105"><wx:templateend start="wx_t2"/>
<table border="1" cellpadding="3" cellspacing="0" id="wx106">
<tr id="wx107">
<th id="wx108">
<p id="wx109">Valore</p>
</th>
<th id="wx110">
<p id="wx111">ASCII</p>
</th>
</tr>

<tr id="wx112">
<td align="center" id="wx113">
<p id="wx114">16</p>
</td>
<td align="center" id="wx115"><tt id="wx116">Q</tt> </td>
</tr>

<tr id="wx117">
<td align="center" id="wx118">
<p id="wx119">17</p>
</td>
<td align="center" id="wx120"><tt id="wx121">R</tt> </td>
</tr>

<tr id="wx122">
<td align="center" id="wx123">
<p id="wx124">18</p>
</td>
<td align="center" id="wx125"><tt id="wx126">S</tt> </td>
</tr>

<tr id="wx127">
<td align="center" id="wx128">
<p id="wx129">19</p>
</td>
<td align="center" id="wx130"><tt id="wx131">T</tt> </td>
</tr>

<tr id="wx132">
<td align="center" id="wx133">
<p id="wx134">20</p>
</td>
<td align="center" id="wx135"><tt id="wx136">U</tt> </td>
</tr>

<tr id="wx137">
<td align="center" id="wx138">
<p id="wx139">21</p>
</td>
<td align="center" id="wx140"><tt id="wx141">V</tt> </td>
</tr>

<tr id="wx142">
<td align="center" id="wx143">
<p id="wx144">22</p>
</td>
<td align="center" id="wx145"><tt id="wx146">W</tt> </td>
</tr>

<tr id="wx147">
<td align="center" id="wx148">
<p id="wx149">23</p>
</td>
<td align="center" id="wx150"><tt id="wx151">X</tt> </td>
</tr>

<tr id="wx152">
<td align="center" id="wx153">
<p id="wx154">24</p>
</td>
<td align="center" id="wx155"><tt id="wx156">Y</tt> </td>
</tr>

<tr id="wx157">
<td align="center" id="wx158">
<p id="wx159">25</p>
</td>
<td align="center" id="wx160"><tt id="wx161">Z</tt> </td>
</tr>

<tr id="wx162">
<td align="center" id="wx163">
<p id="wx164">26</p>
</td>
<td align="center" id="wx165"><tt id="wx166">a</tt> </td>
</tr>

<tr id="wx167">
<td align="center" id="wx168">
<p id="wx169">27</p>
</td>
<td align="center" id="wx170"><tt id="wx171">b</tt> </td>
</tr>

<tr id="wx172">
<td align="center" id="wx173">
<p id="wx174">28</p>
</td>
<td align="center" id="wx175"><tt id="wx176">c</tt> </td>
</tr>

<tr id="wx177">
<td align="center" id="wx178">
<p id="wx179">29</p>
</td>
<td align="center" id="wx180"><tt id="wx181">d</tt> </td>
</tr>

<tr id="wx182">
<td align="center" id="wx183">
<p id="wx184">30</p>
</td>
<td align="center" id="wx185"><tt id="wx186">e</tt> </td>
</tr>

<tr id="wx187">
<td align="center" id="wx188">
<p id="wx189">31</p>
</td>
<td align="center" id="wx190"><tt id="wx191">f</tt> </td>
</tr>
</table>

<wx:template id="wx_t3" pagename="Template:ColBreak" page_id="653969"/></div>
</td>
<td id="wx192">
<div style="margin-right:20px" id="wx193"><wx:templateend start="wx_t3"/>
<table border="1" cellpadding="3" cellspacing="0" id="wx194">
<tr id="wx195">
<th id="wx196">
<p id="wx197">Valore</p>
</th>
<th id="wx198">
<p id="wx199">ASCII</p>
</th>
</tr>

<tr id="wx200">
<td align="center" id="wx201">
<p id="wx202">32</p>
</td>
<td align="center" id="wx203"><tt id="wx204">g</tt> </td>
</tr>

<tr id="wx205">
<td align="center" id="wx206">
<p id="wx207">33</p>
</td>
<td align="center" id="wx208"><tt id="wx209">h</tt> </td>
</tr>

<tr id="wx210">
<td align="center" id="wx211">
<p id="wx212">34</p>
</td>
<td align="center" id="wx213"><tt id="wx214">i</tt> </td>
</tr>

<tr id="wx215">
<td align="center" id="wx216">
<p id="wx217">35</p>
</td>
<td align="center" id="wx218"><tt id="wx219">j</tt> </td>
</tr>

<tr id="wx220">
<td align="center" id="wx221">
<p id="wx222">36</p>
</td>
<td align="center" id="wx223"><tt id="wx224">k</tt> </td>
</tr>

<tr id="wx225">
<td align="center" id="wx226">
<p id="wx227">37</p>
</td>
<td align="center" id="wx228"><tt id="wx229">l</tt> </td>
</tr>

<tr id="wx230">
<td align="center" id="wx231">
<p id="wx232">38</p>
</td>
<td align="center" id="wx233"><tt id="wx234">m</tt> </td>
</tr>

<tr id="wx235">
<td align="center" id="wx236">
<p id="wx237">39</p>
</td>
<td align="center" id="wx238"><tt id="wx239">n</tt> </td>
</tr>

<tr id="wx240">
<td align="center" id="wx241">
<p id="wx242">40</p>
</td>
<td align="center" id="wx243"><tt id="wx244">o</tt> </td>
</tr>

<tr id="wx245">
<td align="center" id="wx246">
<p id="wx247">41</p>
</td>
<td align="center" id="wx248"><tt id="wx249">p</tt> </td>
</tr>

<tr id="wx250">
<td align="center" id="wx251">
<p id="wx252">42</p>
</td>
<td align="center" id="wx253"><tt id="wx254">q</tt> </td>
</tr>

<tr id="wx255">
<td align="center" id="wx256">
<p id="wx257">43</p>
</td>
<td align="center" id="wx258"><tt id="wx259">r</tt> </td>
</tr>

<tr id="wx260">
<td align="center" id="wx261">
<p id="wx262">44</p>
</td>
<td align="center" id="wx263"><tt id="wx264">s</tt> </td>
</tr>

<tr id="wx265">
<td align="center" id="wx266">
<p id="wx267">45</p>
</td>
<td align="center" id="wx268"><tt id="wx269">t</tt> </td>
</tr>

<tr id="wx270">
<td align="center" id="wx271">
<p id="wx272">46</p>
</td>
<td align="center" id="wx273"><tt id="wx274">u</tt> </td>
</tr>

<tr id="wx275">
<td align="center" id="wx276">
<p id="wx277">47</p>
</td>
<td align="center" id="wx278"><tt id="wx279">v</tt> </td>
</tr>
</table>

<wx:template id="wx_t4" pagename="Template:ColBreak" page_id="653969"/></div>
</td>
<td id="wx280">
<div style="margin-right:20px" id="wx281"><wx:templateend start="wx_t4"/>
<table border="1" cellpadding="3" cellspacing="0" id="wx282">
<tr id="wx283">
<th id="wx284">
<p id="wx285">Valore</p>
</th>
<th id="wx286">
<p id="wx287">ASCII</p>
</th>
</tr>

<tr id="wx288">
<td align="center" id="wx289">
<p id="wx290">48</p>
</td>
<td align="center" id="wx291"><tt id="wx292">w</tt> </td>
</tr>

<tr id="wx293">
<td align="center" id="wx294">
<p id="wx295">49</p>
</td>
<td align="center" id="wx296"><tt id="wx297">x</tt> </td>
</tr>

<tr id="wx298">
<td align="center" id="wx299">
<p id="wx300">50</p>
</td>
<td align="center" id="wx301"><tt id="wx302">y</tt> </td>
</tr>

<tr id="wx303">
<td align="center" id="wx304">
<p id="wx305">51</p>
</td>
<td align="center" id="wx306"><tt id="wx307">z</tt> </td>
</tr>

<tr id="wx308">
<td align="center" id="wx309">
<p id="wx310">52</p>
</td>
<td align="center" id="wx311"><tt id="wx312">0</tt> </td>
</tr>

<tr id="wx313">
<td align="center" id="wx314">
<p id="wx315">53</p>
</td>
<td align="center" id="wx316"><tt id="wx317">1</tt> </td>
</tr>

<tr id="wx318">
<td align="center" id="wx319">
<p id="wx320">54</p>
</td>
<td align="center" id="wx321"><tt id="wx322">2</tt> </td>
</tr>

<tr id="wx323">
<td align="center" id="wx324">
<p id="wx325">55</p>
</td>
<td align="center" id="wx326"><tt id="wx327">3</tt> </td>
</tr>

<tr id="wx328">
<td align="center" id="wx329">
<p id="wx330">56</p>
</td>
<td align="center" id="wx331"><tt id="wx332">4</tt> </td>
</tr>

<tr id="wx333">
<td align="center" id="wx334">
<p id="wx335">57</p>
</td>
<td align="center" id="wx336"><tt id="wx337">5</tt> </td>
</tr>

<tr id="wx338">
<td align="center" id="wx339">
<p id="wx340">58</p>
</td>
<td align="center" id="wx341"><tt id="wx342">6</tt> </td>
</tr>

<tr id="wx343">
<td align="center" id="wx344">
<p id="wx345">59</p>
</td>
<td align="center" id="wx346"><tt id="wx347">7</tt> </td>
</tr>

<tr id="wx348">
<td align="center" id="wx349">
<p id="wx350">60</p>
</td>
<td align="center" id="wx351"><tt id="wx352">8</tt> </td>
</tr>

<tr id="wx353">
<td align="center" id="wx354">
<p id="wx355">61</p>
</td>
<td align="center" id="wx356"><tt id="wx357">9</tt> </td>
</tr>

<tr id="wx358">
<td align="center" id="wx359">
<p id="wx360">62</p>
</td>
<td align="center" id="wx361"><tt id="wx362">+</tt> </td>
</tr>

<tr id="wx363">
<td align="center" id="wx364">
<p id="wx365">63</p>
</td>
<td align="center" id="wx366"><tt id="wx367">/</tt> </td>
</tr>
</table>

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<wx:templateend start="wx_t5"/>
<p id="wx368"><br id="wx369"/>
L'algoritmo causa un aumento delle dimensioni dei dati del 33%, poiché ogni gruppo di 3 byte viene convertito in 4 caratteri.</p>

<a id="Esempio_di_conversione" name="Esempio_di_conversione"/>
<wx:section level="3" title="Esempio di conversione" id="wxsec3"><h3 id="wx370">Esempio di conversione</h3>

<p id="wx371">Dati 3 byte di valore 1, 2, 3, partendo dalla loro <a href="/wit/Codice_binario" title="Codice binario" wx:linktype="known" wx:pagename="Codice_binario" wx:page_id="297352" id="wx372">rappresentazione binaria</a>, applichiamo l'algoritmo:<br id="wx373"/>
</p>

<pre id="wx374">
Valori decimali:                          1           2           3
                                          |           |           |
Rappresentazione binaria:             00000001    00000010    00000011
                                        /    \     /    \     /    \
Suddivisione in gruppi da 6 bit:     000000  01  0000  0010  00  000011
                                     |----|  |------|  |------|  |----|
I 4 valori dedotti:                  000000   010000    001000   000011
                                       \/       \/        \/       \/
Il valore decimale:                     0       16         8        3
                                        |        |         |        |
Il valore convertito:                   A        Q         I        D
</pre>

<p id="wx375">Quindi la sequenza di valori (1, 2, 3) viene convertita nella sequenza (AQID)</p>

<p id="wx376">Nel caso in cui i bit non siano multipli di 6, vengono inseriti bit nulli (0) alla fine, e nella codifica viene aggiunto un simbolo '=' per ogni coppia di bit mancanti (massimo da 0 a 2 coppie, basta fare un piccolo ragionamento matematico)</p>

<p id="wx377">Quindi, preso il singolo valore (1), esso viene convertito nella sequenza (AQ==), il singolo valore (2) viene convertito in (Ag==), mentre la sequenza (1, 2) diventa (AQI=)</p>

<p id="wx378"><br id="wx379"/>
<b id="wx380">Una possibile routine di conversione:</b></p>

<pre id="wx381">
union conv
{
    unsigned int l;
    struct bytes
    {
        char b1;
        char b2;
        char b3;
        char b4;
    } b;
};

char convert (char c)
{
    if (c == 63)
        return 47;
    else if (c == 62)
        return 43;
    else if (c &gt;= 52)
        return c - 4;
    else if (c &gt;= 26)
        return c + 71;
    else
        return c + 65;
}

unsigned int toBase64(char b1, char b2, char b3)
{
    conv src, dest;
    src.b.b1 = b3;
    src.b.b2 = b2;
    src.b.b3 = b1;
    src.b.b4 = 0;
    //conv.l == b4 b3 b2 b1
    dest.b.b1 = convert(src.b.b1 &amp; 0x3f);
    src.l = src.l &gt;&gt; 6;
    dest.b.b2 = convert(src.b.b1 &amp; 0x3f);
    src.l = src.l &gt;&gt; 6;
    dest.b.b3 = convert(src.b.b1 &amp; 0x3f);
    src.l = src.l &gt;&gt; 6;
    dest.b.b4 = convert(src.b.b1 &amp; 0x3f);

    return dest.l;
}
</pre>

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<p id="wx389">:  accedi alle voci di Wikipedia che parlano di matematica</p>
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<a href="/wit/index.php?title=Speciale:Categories&amp;article=Base64" title="Speciale:Categories" wx:linktype="known" wx:pagename="Speciale:Categories" id="wx390">Categorie</a>: <span dir="ltr" id="wx391"><a href="/wit/Categoria:Sistemi_di_numerazione" title="Categoria:Sistemi di numerazione" wx:linktype="known" wx:pagename="Categoria:Sistemi_di_numerazione" wx:page_id="41168" id="wx392">Sistemi di numerazione</a></span> | <span dir="ltr" id="wx393"><a href="/wit/Categoria:Algoritmi_numerici" title="Categoria:Algoritmi numerici" wx:linktype="known" wx:pagename="Categoria:Algoritmi_numerici" wx:page_id="249916" id="wx394">Algoritmi numerici</a></span></div>
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Altre lingue: <a href="http://cs.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="cs:Base64" id="wx395">Česky</a> | <a href="http://da.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="da:Base64" id="wx396">Dansk</a> | <a href="http://de.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="de:Base64" id="wx397">Deutsch</a> | <a href="http://en.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="en:Base64" id="wx398">English</a> | <a href="http://es.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="es:Base64" id="wx399">Español</a> | <a href="http://fr.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="fr:Base64" id="wx400">Français</a> | <a href="http://hu.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="hu:Base64" id="wx401">Magyar</a> | <a href="http://ja.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="ja:Base64" id="wx402">日本語</a> | <a href="http://ko.wikipedia.org/wiki/%EB%B2%A0%EC%9D%B4%EC%8A%A464" class="external" wx:linktype="interwiki" wx:pagename="ko:베이스64" id="wx403">한국어</a> | <a href="http://nl.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="nl:Base64" id="wx404">Nederlands</a> | <a href="http://pl.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="pl:Base64" id="wx405">Polski</a> | <a href="http://pt.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="pt:Base64" id="wx406">Português</a> | <a href="http://ru.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="ru:Base64" id="wx407">Русский</a> | <a href="http://sk.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="sk:Base64" id="wx408">Slovenčina</a> | <a href="http://sr.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="sr:Base64" id="wx409">Српски / Srpski</a> | <a href="http://sv.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="sv:Base64" id="wx410">Svenska</a> | <a href="http://tr.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="tr:Base64" id="wx411">Türkçe</a> | <a href="http://yi.wikipedia.org/wiki/%D7%91%D7%A2%D7%99%D7%A1_64" class="external" wx:linktype="interwiki" wx:pagename="yi:בעיס_64" id="wx412">ייִדיש</a> | <a href="http://zh.wikipedia.org/wiki/Base64" class="external" wx:linktype="interwiki" wx:pagename="zh:Base64" id="wx413">中文</a></div>
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