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	<id>https://nick-black.com/dankwiki/index.php?action=history&amp;feed=atom&amp;title=Combinatorial_devices</id>
	<title>Combinatorial devices - revision history</title>
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	<updated>2026-07-11T16:14:58Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://nick-black.com/dankwiki/index.php?title=Combinatorial_devices&amp;diff=2583&amp;oldid=prev</id>
		<title>Dank at 19:32, 22 March 2010</title>
		<link rel="alternate" type="text/html" href="https://nick-black.com/dankwiki/index.php?title=Combinatorial_devices&amp;diff=2583&amp;oldid=prev"/>
		<updated>2010-03-22T19:32:51Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw-interface=&quot;&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:32, 22 March 2010&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot;&gt;Line 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The circuit contains no directed cycles.&amp;lt;/blockquote&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The circuit contains no directed cycles.&amp;lt;/blockquote&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Each output of a composed combinatorial device has its own &amp;#039;&amp;#039;t&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt;, equal to the maxmium cumulative propagation delays encountered on any path from an input to that output.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Each output of a composed combinatorial device has its own &amp;#039;&amp;#039;t&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt;, equal to the maxmium cumulative propagation delays encountered on any path from an input to that output.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[CATEGORY: Hardware]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Dank</name></author>
	</entry>
	<entry>
		<id>https://nick-black.com/dankwiki/index.php?title=Combinatorial_devices&amp;diff=2582&amp;oldid=prev</id>
		<title>Dank at 19:32, 22 March 2010</title>
		<link rel="alternate" type="text/html" href="https://nick-black.com/dankwiki/index.php?title=Combinatorial_devices&amp;diff=2582&amp;oldid=prev"/>
		<updated>2010-03-22T19:32:11Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw-interface=&quot;&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:32, 22 March 2010&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l4&quot;&gt;Line 4:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 4:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A &amp;#039;&amp;#039;functional specification&amp;#039;&amp;#039;, detailing the value of each output for each of the possible combinations of input values; and&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A &amp;#039;&amp;#039;functional specification&amp;#039;&amp;#039;, detailing the value of each output for each of the possible combinations of input values; and&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A &amp;#039;&amp;#039;timing specification&amp;#039;&amp;#039;, consisting (at minimum) of an upper bound &amp;#039;&amp;#039;t&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt; on the time required for the device to compute the specified output values from an arbitrary set of input values.&amp;lt;/blockquote&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* A &amp;#039;&amp;#039;timing specification&amp;#039;&amp;#039;, consisting (at minimum) of an upper bound &amp;#039;&amp;#039;t&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt; on the time required for the device to compute the specified output values from an arbitrary set of input values.&amp;lt;/blockquote&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Combinatorial devices are closed under combinatorial composition:&amp;lt;blockquote&amp;gt;A circuit is a combinatorial device if it consists of interconnected circuit elements such that:&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;t&#039;&#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt; is known as the &#039;&#039;propagation delay&#039;&#039; of a device, and interpreted as a maximum time before outputs reflect the provided inputs (a minimum delay, if specified, is known as &#039;&#039;contamination delay&#039;&#039;). Thus, inputs provided and maintained for &#039;&#039;t&#039;&#039; seconds can be read for at least &#039;&#039;t&#039;&#039; - &#039;&#039;t&#039;&#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt; seconds. &lt;/ins&gt;Combinatorial devices are closed under combinatorial composition:&amp;lt;blockquote&amp;gt;A circuit is a combinatorial device if it consists of interconnected circuit elements such that:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Each circuit element is itself combinatorial,&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Each circuit element is itself combinatorial,&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Every node of the circuit is either designated as an input to the circuit or connects to exactly one output terminal of the circuit element, and&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Every node of the circuit is either designated as an input to the circuit or connects to exactly one output terminal of the circuit element, and&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The circuit contains no directed cycles.&amp;lt;/blockquote&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The circuit contains no directed cycles.&amp;lt;/blockquote&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Each output of a composed combinatorial device has its own &#039;&#039;t&#039;&#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt;, equal to the maxmium cumulative propagation delays encountered on any path from an input to that output.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Dank</name></author>
	</entry>
	<entry>
		<id>https://nick-black.com/dankwiki/index.php?title=Combinatorial_devices&amp;diff=2581&amp;oldid=prev</id>
		<title>Dank: Created page with &#039;Lifting a definition from Ward and Halstead&#039;s &#039;&#039;Computation Structures&#039;&#039; (ISBN 0-262-23139-5), pp4--5:&lt;blockquote&gt;A combinatorial device is a circuit element have the following p...&#039;</title>
		<link rel="alternate" type="text/html" href="https://nick-black.com/dankwiki/index.php?title=Combinatorial_devices&amp;diff=2581&amp;oldid=prev"/>
		<updated>2010-03-22T19:27:06Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;#039;Lifting a definition from Ward and Halstead&amp;#039;s &amp;#039;&amp;#039;Computation Structures&amp;#039;&amp;#039; (ISBN 0-262-23139-5), pp4--5:&amp;lt;blockquote&amp;gt;A combinatorial device is a circuit element have the following p...&amp;#039;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;Lifting a definition from Ward and Halstead&amp;#039;s &amp;#039;&amp;#039;Computation Structures&amp;#039;&amp;#039; (ISBN 0-262-23139-5), pp4--5:&amp;lt;blockquote&amp;gt;A combinatorial device is a circuit element have the following properties:&lt;br /&gt;
* One or more discrete-valued &amp;#039;&amp;#039;input&amp;#039;&amp;#039; terminals;&lt;br /&gt;
* One or more discrete-valued &amp;#039;&amp;#039;output&amp;#039;&amp;#039; terminals;&lt;br /&gt;
* A &amp;#039;&amp;#039;functional specification&amp;#039;&amp;#039;, detailing the value of each output for each of the possible combinations of input values; and&lt;br /&gt;
* A &amp;#039;&amp;#039;timing specification&amp;#039;&amp;#039;, consisting (at minimum) of an upper bound &amp;#039;&amp;#039;t&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;pd&amp;lt;/sub&amp;gt; on the time required for the device to compute the specified output values from an arbitrary set of input values.&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
Combinatorial devices are closed under combinatorial composition:&amp;lt;blockquote&amp;gt;A circuit is a combinatorial device if it consists of interconnected circuit elements such that:&lt;br /&gt;
* Each circuit element is itself combinatorial,&lt;br /&gt;
* Every node of the circuit is either designated as an input to the circuit or connects to exactly one output terminal of the circuit element, and&lt;br /&gt;
* The circuit contains no directed cycles.&amp;lt;/blockquote&amp;gt;&lt;/div&gt;</summary>
		<author><name>Dank</name></author>
	</entry>
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