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1010 + 0111 = 10001
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<!--replace-end-7--><!--replace-end-4--><!--replace-end-1--></head><body><div class="ui fluid container universe"><!--replace-start-2--><!--replace-start-3--><!--replace-start-6--><div class="ui text container" id="zettel-container" style="position: relative"><div class="zettel-view"><article class="ui raised attached segment zettel-content"><div class="pandoc"><h1 id="title-h1">Binary addition</h1><ul><li>We add binary values in columns just like we would with denary addition.</li><li>Each column is classified on the basis of place-value. In denary this is 10, in binary it is 2.</li><li>When we conduct a binary addition, we add the binary values as if they were normal integers but we represent the sums as binary.<ul><li>For example: <span class="math inline">\(1 + 1 = 2\)</span> for the calculation but the sum is <span class="math inline">\(10\)</span></li></ul></li></ul><h2 id="examples">Examples</h2><h3 id="example-one">Example one</h3><p><span class="math display">$$
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1010 + 0111 = 10001
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$$</span></p><p><span class="math display">$$
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10 + 7 = 17
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$$</span></p><p>In the first column: <span class="math inline">\(1 + 0 = 1\)</span>, so we simply put the binary value for <span class="math inline">\(1\)</span>:</p><pre><code class="language-none">1010
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0111
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____
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1</code></pre><p>In the second column: <span class="math inline">\(1 + 1 = 2\)</span>. In binary this is represented as <span class="math inline">\(10\)</span>. So we put <span class="math inline">\(0\)</span> beneath the bar and carry the <span class="math inline">\(1\)</span>:</p><pre><code class="language-none"> 1
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1010
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0111
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____
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01</code></pre><p>In the third column, we repeat the previous process. We are presented with <span class="math inline">\(1 + 0 + 1\)</span> which is <span class="math inline">\(2\)</span>. As <span class="math inline">\(2\)</span> is <span class="math inline">\(10\)</span> in binary, we put the zero beneath the line and carry the <span class="math inline">\(1\)</span>:</p><pre><code class="language-none">11
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1010
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0111
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____
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001</code></pre><p>In the final column, we again have <span class="math inline">\(1+1\)</span> giving us <span class="math inline">\(2\)</span> or <span class="math inline">\(10\)</span> but at this point we cannot carry any more because we have reached the final column. So instead of carrying the <span class="math inline">\(1\)</span> we just put both digits beneath the line <span class="math inline">\(10\)</span>.</p><pre><code class="language-none"> 11
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1010
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0111
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_____
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10001</code></pre><h3 id="example-two">Example two</h3><p><span class="math display">$$
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1001 + 0111 = 10000
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$$</span></p><p><span class="math display">$$
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9 + 7 = 16
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$$</span></p><pre><code class="language-none"> 111
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1001
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0111
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_____
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10000</code></pre></div></article><nav class="ui attached segment deemphasized backlinksPane" id="neuron-backlinks-pane"><h3 class="ui header">Backlinks</h3><ul class="backlinks"><li><span class="zettel-link-container cf"><span class="zettel-link"><a href="Twos_complement.html">Two’s complement</a></span></span><ul class="context-list" style="zoom: 85%;"><li class="item"><div class="pandoc"><p><span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Signed and unsigned numbers"><a href="Signed_and_unsigned_numbers.html">signed_and_unsigned_numbers</a></span></span>, <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Binary addition"><a href="Binary_addition.html">binary addition</a></span></span>, <span class="zettel-link-container cf"><span class="zettel-link"><a href="Signed_magnitude_representation.html">Signed magnitude representation</a></span></span></p></div></li></ul></li></ul></nav><nav class="ui attached segment deemphasized bottomPane" id="neuron-tags-pane"><div><span class="ui basic label zettel-tag" title="Tag">binary</span></div></nav><nav class="ui bottom attached icon compact inverted menu blue" id="neuron-nav-bar"><!--replace-start-9--><!--replace-end-9--><a class="right item" href="impulse.html" title="Open Impulse"><i class="wave square icon"></i></a></nav></div></div><!--replace-end-6--><!--replace-end-3--><!--replace-end-2--><div class="ui center aligned container footer-version"><div class="ui tiny image"><a href="https://neuron.zettel.page"><img alt="logo" src="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" title="Generated by Neuron 1.9.35.3" /></a></div></div></div></body></html> |