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<section id="numpy-binary-repr">
<h1>numpy.binary_repr<a class="headerlink" href="#numpy-binary-repr" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="numpy.binary_repr">
<span class="sig-prename descclassname"><span class="pre">numpy.</span></span><span class="sig-name descname"><span class="pre">binary_repr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">num</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">width</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/main/numpy/_core/numeric.py#L2014-L2119"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#numpy.binary_repr" title="Link to this definition">#</a></dt>
<dd><p>Return the binary representation of the input number as a string.</p>
<p>For negative numbers, if width is not given, a minus sign is added to the
front. If width is given, the two’s complement of the number is
returned, with respect to that width.</p>
<p>In a two’s-complement system negative numbers are represented by the two’s
complement of the absolute value. This is the most common method of
representing signed integers on computers <a class="reference internal" href="#r962252997619-1" id="id1">[1]</a>. A N-bit two’s-complement
system can represent every integer in the range
<span class="math notranslate nohighlight">\(-2^{N-1}\)</span> to <span class="math notranslate nohighlight">\(+2^{N-1}-1\)</span>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>num</strong><span class="classifier">int</span></dt><dd><p>Only an integer decimal number can be used.</p>
</dd>
<dt><strong>width</strong><span class="classifier">int, optional</span></dt><dd><p>The length of the returned string if <em class="xref py py-obj">num</em> is positive, or the length
of the two’s complement if <em class="xref py py-obj">num</em> is negative, provided that <em class="xref py py-obj">width</em> is
at least a sufficient number of bits for <em class="xref py py-obj">num</em> to be represented in
the designated form. If the <em class="xref py py-obj">width</em> value is insufficient, an error is
raised.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>bin</strong><span class="classifier">str</span></dt><dd><p>Binary representation of <em class="xref py py-obj">num</em> or two’s complement of <em class="xref py py-obj">num</em>.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.base_repr.html#numpy.base_repr" title="numpy.base_repr"><code class="xref py py-obj docutils literal notranslate"><span class="pre">base_repr</span></code></a></dt><dd><p>Return a string representation of a number in the given base system.</p>
</dd>
<dt><a class="reference external" href="https://docs.python.org/3/library/functions.html#bin" title="(in Python v3.13)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">bin</span></code></a></dt><dd><p>Python’s built-in binary representation generator of an integer.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p><a class="reference internal" href="#numpy.binary_repr" title="numpy.binary_repr"><code class="xref py py-obj docutils literal notranslate"><span class="pre">binary_repr</span></code></a> is equivalent to using <a class="reference internal" href="numpy.base_repr.html#numpy.base_repr" title="numpy.base_repr"><code class="xref py py-obj docutils literal notranslate"><span class="pre">base_repr</span></code></a> with base 2, but about 25x
faster.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r962252997619-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p>Wikipedia, “Two’s complement”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Two's_complement">https://en.wikipedia.org/wiki/Two’s_complement</a></p>
</div>
</div>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="313e21a7-538f-4eb6-9c4d-14c264e33d6a">
<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('313e21a7-538f-4eb6-9c4d-14c264e33d6a','a40d4d4f-ab27-419e-8ca8-ce41df64b24a','d63d5cd5-9ecb-497c-9399-9671205f5f8f','../../lite/tree/../notebooks/index.html?path=2c187b89_c455_4142_9b36_155c9a3a9c60.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">binary_repr</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="go">'11'</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">binary_repr</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">)</span>
<span class="go">'-11'</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">binary_repr</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
<span class="go">'0011'</span>
</pre></div>
</div>
<p>The two’s complement is returned when the input number is negative and
width is specified:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">binary_repr</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="go">'101'</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">binary_repr</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<span class="go">'11101'</span>
</pre></div>
</div>
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