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<title>Serial binary adder</title>
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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Serial binary adder</span></span>
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<p>The <b>serial binary adder</b> or <b>bit-serial adder</b> is a <a href="Digital_circuit" class="mw-redirect" title="Digital circuit">digital circuit</a> that performs <a href="Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a> <a href="Binary_adder" class="mw-redirect" title="Binary adder">addition</a> bit by bit. The serial <a href="Full_adder" class="mw-redirect" title="Full adder">full adder</a> has three single-bit inputs for the numbers to be added and the carry in. There are two single-bit outputs for the sum and carry out. The carry-in signal is the previously calculated carry-out signal. The addition is performed by adding each bit, lowest to highest, one per clock cycle.
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<div class="mw-heading mw-heading2"><h2 id="Serial_binary_addition">Serial binary addition</h2></div>
<p>Serial binary addition is done by a <a href="Flip-flop_(electronics)" title="Flip-flop (electronics)">flip-flop</a> and a <a href="Full_adder" class="mw-redirect" title="Full adder">full adder</a>. The flip-flop takes the carry-out signal on each clock cycle and provides its value as the carry-in signal on the next clock cycle. After all of the bits of the input operands have arrived, all of the bits of the sum have come out of the sum output.
</p>
<div class="mw-heading mw-heading2"><h2 id="Serial_binary_subtractor">Serial binary subtractor</h2></div>
<p>The serial binary <a href="Subtractor_(electronics)" class="mw-redirect" title="Subtractor (electronics)">subtractor</a> operates the same as the serial binary adder, except the subtracted number is converted to its <a href="Two's_complement" title="Two's complement">two's complement</a> before being added. Alternatively, the number to be subtracted is converted to its <a href="Ones'_complement" title="Ones' complement">ones' complement</a>, by inverting its bits, and the carry flip-flop is initialized to a 1 instead of to 0 as in addition. The ones' complement plus the 1 is the two's complement.
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<div class="mw-heading mw-heading2"><h2 id="Example_of_operation">Example of operation</h2></div>
<dl><dt>Decimal</dt>
<dd>5+9=14
<ul><li>X=5, Y=9, Sum=14</li></ul></dd></dl>
<dl><dt>Binary</dt>
<dd>0101+1001=1110</dd></dl>
<dl><dt>Addition of each step</dt></dl>
<table class="wikitable">
<tbody><tr>
<th colspan="3">Inputs
</th>
<th colspan="2">Outputs
</th></tr>
<tr>
<th width="30">Cin
</th>
<th width="30">X
</th>
<th width="30">Y
</th>
<th width="30">Sum
</th>
<th width="30">Cout
</th></tr>
<tr>
<td>0
</td>
<td>1
</td>
<td>1
</td>
<td>0
</td>
<td>1
</td></tr>
<tr>
<td>1
</td>
<td>0
</td>
<td>0
</td>
<td>1
</td>
<td>0
</td></tr>
<tr>
<td>0
</td>
<td>1
</td>
<td>0
</td>
<td>1
</td>
<td>0
</td></tr>
<tr>
<td>0
</td>
<td>0
</td>
<td>1
</td>
<td>1
</td>
<td>0
</td></tr></tbody></table>
<p><i>*addition starts from <a href="Bit_numbering" title="Bit numbering">LSb</a></i>
</p>
<dl><dt>Result=1110 or 14</dt></dl>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Parallel_binary_adder" class="mw-redirect" title="Parallel binary adder">Parallel binary adder</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
<ul><li><a rel="nofollow" class="external free" href="http://www.quinapalus.com/wires8.html">http://www.quinapalus.com/wires8.html</a></li>
<li><a rel="nofollow" class="external free" href="http://www.asic-world.com/digital/arithmetic3.html">http://www.asic-world.com/digital/arithmetic3.html</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
<ul><li><a rel="nofollow" class="external text" href="http://teahlab.com/finite_state_machine_Serial_Adder/">Interactive Serial Adder</a>, Provides the visual logic of the Serial Adder circuit built with Teahlab's Simulator.</li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
This article is issued from <a class="external text" title="Last edited on 2024-10-13" href="https://en.wikipedia.org/wiki/?title=Serial_binary_adder&oldid=1250968390">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.
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