5973 /www/nrich/html/content/id/5973/ 1 2011-02-01T00:00:01 <mdoxml version="1.0"><br></br> In this problem a circuit has been set up. There are two switches on the left, two logic gates in the middle and two bulbs on the right.<br></br> <br></br> Currently the gates are both set to XOR. They can be changed to any of the following: AND, NAND, OR, NOR, XNOR. Any switch or gate can be altered by clicking on the blue square in its top left hand corner. If you are unsure about the meaning of the logic gates, take a look at <a href="http://nrich.maths.org/public/viewer.php?obj_id=5974&amp;part=">Circuit Maker</a> <br></br> <br></br> Can you set the gates so that the number of bulbs which are on is the same as the number of switches which are on? In other words: <br></br> <div style="margin-left: 40px;">when both switches are off both bulbs are off,<br></br> when either switch is on one bulb is on,<br></br> when both switches are on both bulbs are on.</div> <br></br> <a href="/content/id/5973/Circuits%20adder%202.swf">Full Screen Version</a> <br></br> <mdo:flash height="400" width="560"><param value="/content/id/5973/Circuits%20adder%202.swf" name="movie" ></param><param value="8" name="flashplayerversion" ></param></mdo:flash><br></br> <br></br> <span style="font-weight: bold;">Other circuits to try to construct</span> <br></br> <br></br> Can you set the gates so that: <br></br> <br></br> <div style="margin-left: 40px;">when both switches are on both bulbs are on,</div> <div style="margin-left: 40px;">the rest of the time - both bulbs are off;</div> <br></br> <div style="margin-left: 40px;">when both switches are off both bulbs are on,</div> <div style="margin-left: 40px;">the rest of the time - both bulbs are off;</div> <br></br> <div style="margin-left: 40px;">when both switches are off both bulbs are off,</div> <div style="margin-left: 40px;">when one switch is on both bulbs are on,</div> <div style="margin-left: 40px;">when both switches are on one bulb is on.</div> <br></br> Experiment further with the effects of the different settings to create similar problems: choose a setting for the two gates, describe clearly the effect of your circuit and challenge a partner to figure out your settings.<br></br> <br></br> If you liked this problem you may like to build your own circuit boards with interesting properties using the <a href="http://nrich.maths.org/public/viewer.php?obj_id=5974&amp;part=">Circuit Maker</a> interactivity, or try the harder <a href="http://nrich.maths.org/public/viewer.php?obj_id=5931&amp;part=">Adding Machine</a> problem. <br></br></mdoxml> <mdoxml version="1.0"><br></br> <p><span class="editorial">Well done to Chris from CSN for a clear explanation on how to solve the first question, and well done to Jake from Crosscrake C.E. School, Louise from Melling St.Wilfreds School and Tristan from St James School for answering the first three questions correctly. Special congratulations go to Rachel from Tatham Fells School who managed to answer all questions correctly. Here are her solutions:</span></p> <br></br> <span style="font-weight: bold;">With OR and AND for the switches:</span> <br></br> <br></br> when both switches are off both bulbs are off, <br></br> when either switch is on one bulb is on, <br></br> when both switches are on both bulbs are on.<br></br> <br></br> <br></br> <span style="font-weight: bold;">With AND and AND for the switches:</span> <br></br> <br></br> when both switches are on both bulbs are on, <br></br> the rest of the time - both bulbs are off.<br></br> <br></br> <br></br> <span style="font-weight: bold;">With NOR and NOR for the switches:</span> <br></br> <br></br> when both switches are off both bulbs are on, <br></br> the rest of the time - both bulbs are off.<br></br> <br></br> <br></br> <span style="font-weight: bold;">With XOR and OR for the switches:</span> <br></br> <br></br> when both switches are off both bulbs are off, <br></br> when one switch is on both bulbs are on, <br></br> when both switches are on one bulb is on.<br></br></mdoxml> <mdoxml version="1.0"><br></br> <h3>Why do this problem?</h3> This problem offers a simple challenge using logic gates and circuits. Through experimentation with switches and settings, students will begin to see the structure of logic gates emerge without the need for any detailed formalism. They can then move on to construct circuits with more complicated behaviours.<br></br> <h3>Possible approach</h3> <div>If students haven't worked with logic gates before you could start by directing them to <a href="http://nrich.maths.org/public/viewer.php?obj_id=5974&amp;part=">Circuit Maker</a></div> <br></br> <div>Put the problem on to the board. Ask students to work out what the circuit board does.</div> <br></br> <div>Encourage experimentation with combinations of on / off switches and different settings on the logic gates. At each stage, encourage students to predict what they think will happen, and to explain what does happen.</div> <h3>Key questions</h3> Describe what you see.<br></br> What can we change? <br></br> What will happen if we change the settings?<br></br> <h3>Possible extension</h3> Once the concept of the gate is understood there are several follow up problems, such as <a href="http://nrich.maths.org/public/viewer.php?obj_id=5931&amp;part=">Adding Machine</a> <br></br> <h3>Possible support</h3> You might suggest focussing on the AND and OR gates to begin with.<br></br> <br></br></mdoxml> <mdoxml version="1.0"><br></br> Take a look at <a href="http://nrich.maths.org/public/viewer.php?obj_id=5974&amp;part=">Circuit Maker</a> and experiment with the interactivity provided.<br></br> <br></br> There is more information on Logic Gates <a href="http://www.kpsec.freeuk.com/gates.htm">here</a> <br></br> <br></br></mdoxml> <mdoxml version="1.0"> <br></br> Settings: AND and OR for the two gates<br></br>  <br></br> s<a href="/content/id/5973/Circuits%20adder%202.swf">w</a>f<br></br>  <br></br> </mdoxml> 2 4 0 0 1 0 0 Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on? 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