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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">3-bit Counter</h1><p>To demonstrate the use of <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Flip-Flops"><a href="Flip_flops.html">Flip-Flops</a></span></span> we will create the circuit for a 3-bit counter. This simply counts up from 0 to 7 because 7 is the maximum decimal number we can create with three bits (<span class="math inline">\(2^3\)</span>):</p><table class="ui table"><thead><tr><th>Binary</th><th>Decimal</th></tr></thead><tbody><tr><td>000</td><td>0</td></tr><tr><td>001</td><td>1</td></tr><tr><td>010</td><td>2</td></tr><tr><td>011</td><td>3</td></tr><tr><td>100</td><td>4</td></tr><tr><td>101</td><td>5</td></tr><tr><td>110</td><td>6</td></tr><tr><td>111</td><td>7</td></tr></tbody></table><p>The circuit will have three memory components, each representing one bit of the 3-bit number. When the <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Clock signals"><a href="Clock_signals.html">clock pulses</a></span></span>, the 3-bit number increments by one. We need to synchronise the operation with a clock because each bit by itself is meaningless, it only gains meaning by the relation it sustains to the other two bits hence it must be kept in sync with them.</p><p>We can derive the circuit arrangement by analysing the outputs of a flipflop at each pulse:</p><table class="ui table"><thead><tr><th>Combined bits</th><th>Q2</th><th>Q1</th><th>Q0</th><th>Decimal</th></tr></thead><tbody><tr><td>000</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>001</td><td>0</td><td>0</td><td>1</td><td>1</td></tr><tr><td>010</td><td>0</td><td>1</td><td>0</td><td>2</td></tr><tr><td>011</td><td>0</td><td>1</td><td>1</td><td>3</td></tr><tr><td>100</td><td>1</td><td>0</td><td>0</td><td>4</td></tr><tr><td>101</td><td>1</td><td>0</td><td>1</td><td>5</td></tr><tr><td>110</td><td>1</td><td>1</td><td>0</td><td>6</td></tr><tr><td>111</td><td>1</td><td>1</td><td>1</td><td>7</td></tr></tbody></table><p>If we look at the pattern of each flip-flops’ output we notice the following:</p><ul><li><em>Q0</em> toggles on every pulse</li><li><em>Q1</em> toggles every time <em>Q0</em> was previously 1</li><li><em>Q2</em> toggles when both <em>Q1</em> and <em>Q0</em> were previously 1</li></ul><p>This means that to construct a circuit that displays this behaviour we just have to use a <a href="Flip_flops.md#t-flip-flops">T flip-flop</a> since the only state change we need is a single bit toggle three times that retains its value.</p><p>Using these pulse patterns we can construct a circuit as follows: <img src="/static/3-bit-adder-diagram.png" /></p><iframe src="https://circuitverse.org/simulator/embed/3-bit-counter-d33846e3-7538-427d-b4cc-dc64fdaf0af3?theme=default&display_title=false&clock_time=true&fullscreen=true&zoom_in_out=true" style="border-width:; border-style: solid; border-color:;" name="myiframe" id="projectPreview" scrolling="no" frameborder="1" marginheight="0px" marginwidth="0px" height="500" width="600" allowFullScreen></iframe>
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<blockquote><p>Remember from the table: Q2 is the most significant bit and Q0 is the least significant bit so we should read the output in the interactive circuit backwards, reversing the order. Then we will see that the cicuit is cyling through 0-7</p></blockquote><p>This is how the circuit works:</p><ul><li>All three flip-flops are connected to the same clock signal so that they are synchnonised</li><li>Because <em>T0</em> is connected to the voltage source <em>Q0</em> toggles every time the clock pulses</li><li><em>T1</em> is connected to <em>Q0</em> so a clock pulse causes <em>Q1</em> to toggle only when <em>Q0</em> is high in line with the table</li><li><em>T2</em> is connected to <em>Q0 AND Q1</em> so <em>Q2</em> only toggles on a clock pulse when <em>Q0</em> and <em>Q1</em> are both high</li></ul></div></article><nav class="ui attached segment deemphasized bottomPane" id="neuron-tags-pane"><div><span class="ui basic label zettel-tag" title="Tag">binary</span><span class="ui basic label zettel-tag" title="Tag">logic-gates</span><span class="ui basic label zettel-tag" title="Tag">memory</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> |