8260
/www/nrich/html/content/id/8260/
6
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>A circuit is a set of switches, wires, bulbs and components called <span style="font-style: italic;">logic gates</span> .<br></br>
<br></br>
There are seven different types of logic gates, each with a technical-sounding name:</p>
<div style="margin-left: 40px;">AND</div>
<div style="margin-left: 40px;">OR</div>
<div style="margin-left: 40px;">XOR (exclusively OR)</div>
<div style="margin-left: 40px;">NAND (not AND)</div>
<div style="margin-left: 40px;">NOR (not OR)</div>
<div style="margin-left: 40px;">XNOR (not XOR)</div>
<div style="margin-left: 40px;">NOT</div>
<br></br>
<p>One wire comes out of each logic gate and in the examples below this wire is always attached to a bulb. The bulb is on or off depending on the inputs from the switches and the type of logic gate.<br></br>
<br></br>
Here is a circuit containing one of each type of gate wired up to a bulb.<br></br>
<br></br>
By clicking the switches on or off (using the blue square in their top left hand corners), can you work out what each of the different logic gates does?<br></br>
<br></br>
<a href="/content/id/5974/Simple%20Adding.swf">Full Screen Version</a><br></br>
<mdo:flash height="400" id="/content/id/8260//content/id/5974/Simple%20Adding.swf" width="560"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/5974/Simple%20Adding.swf"></param>
<param name="flashplayerversion" value="8"></param>
</mdo:flash><br></br>
<br></br>
Now that you are familiar with the properties of the gates you can experiment by building your own circuits with interesting properties using the interactivity below. Instructions are given at the bottom of the page. You can find some ideas and challenges in <a href="http://nrich.maths.org/public/viewer.php?obj_id=5973&part=">Simple Counting Machine</a><br></br>
<br></br>
You can also read and learn more about logic circuits and gates and mathematical logic in the article <a href="http://nrich.maths.org/public/viewer.php?obj_id=6023&part=index">Logic, Truth Tables and Switching Circuits</a> <a href="http://nrich.maths.org/public/viewer.php?obj_id=6023&part=index">.</a><br></br>
<br></br>
<a href="/content/id/5974/Circuits.swf">Full Screen Version</a><br></br>
<mdo:flash height="400" id="/content/id/8260//content/id/5974/Circuits.swf" width="560"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/5974/Circuits.swf"></param>
<param name="flashplayerversion" value="8"></param>
</mdo:flash></p>
<div class="framework"><br></br>
INSTRUCTIONS<br></br>
<br></br>
<br></br>
To build a circuit follow these steps. You can delete mistakes by clicking on the cross which appears when you hover above the icon.<br></br>
<br></br>
1. Left-click on the components to drag them on to the circuit board space.<br></br>
<br></br>
2. FIRST click next to a red dot and drag to the right to create a wire; THEN you can stretch this wire to join with any other red dot in the circuit.<br></br>
<br></br>
3. Click on the switches to turn them on or off. Wires 'fill' with current unless blocked by an un-triggered logic gate.<br></br>
<br></br>
4. Click on the logic gates to change their type.<br></br>
<br></br>
5. Left-click and drag to move the components around.<br></br>
<br></br>
The key ideas are shown in this picture; by clicking on the triangle you can also watch a short video clip (1Mb) of the creation of the circuit.<br></br>
<br></br>
<div id="fix"> </div>
<script type="text/javascript">
//
//
var vid = document.createElement('video');
//vid.setAttribute('height', '640');
//vid.setAttribute('width', '480');
vid.setAttribute('controls', 'controls');
var link = document.createElement('source');
link.setAttribute('src', '/content/id/8260/video.mp4');
link.setAttribute('type', 'video/mp4');
vid.appendChild(link);
document.getElementById("fix").appendChild(vid);
//
//
</script></div>
<br></br>
<br></br>
<br></br>
<p><a href="/content/id/5681/Manipulatives.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_01.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_19.flv">Download Link</a> <a href="/content/id/6940/Stage3Final.flv">Download Link</a> <a href="/content/id/%205746/TangleSymmetry.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_02.flv">Download
Link</a> <a href="/content/id/6307/AutoScreenRecorder_20.flv">Download Link</a> <a href="/content/id/6940/TeacherIntro3.flv">Download Link</a> <a href="/content/id/%205775/Video.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_03.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_21.flv">Download Link</a> <a href="/content/id/6961/Stage3Final.flv">Download
Link</a> <a href="/content/id/%205776/Conway.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_04.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_22.flv">Download Link</a> <a href="/content/id/6961/TeacherIntro3.flv">Download Link</a> <a href="/content/id/%205835/Video.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_05.flv">Download
Link</a> <a href="/content/id/6307/AutoScreenRecorder_23.flv">Download Link</a> <a href="/content/id/7013/jo2.flv">Download Link</a> <a href="/content/id/%205861/Video.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_06.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_24.flv">Download Link</a> <a href="/content/id/7013/jocropped.flv">Download Link</a>
<a href="/content/id/%205869/ImpossibleSquare.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_07.flv">Download Link</a> <a href="/content/id/6806/FranVid.flv">Download Link</a> <a href="/content/id/7369/FranIntro.flv">Download Link</a> <a href="/content/id/%205885/Video.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_08.flv">Download Link</a> <a href="/content/id/6806/MakingUnits.flv">Download Link</a> <a href="/content/id/7369/FranVid.flv">Download Link</a> <a href="/content/id/%205885/WhatsAKnot.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_09.flv">Download Link</a> <a href="/content/id/6806/PentagonsVertices.flv">Download Link</a> <a href="/content/id/7392/BryonyTriangle.flv">Download Link</a> <a href="/content/id/%205886/Video.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_10.flv">Download Link</a> <a href="/content/id/6806/WholePolyhedraSpeededUp.flv">Download Link</a> <a href="/content/id/7459/HELICOPTER.flv">Download Link</a> <a href="/content/id/%205901/TangleSymmetry.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_11.flv">Download Link</a>
<a href="/content/id/6835/Video.flv">Download Link</a> <a href="/content/id/7511/Clip%201%20Polyplugrectangles.flv">Download Link</a> <a href="/content/id/%205923/ImpossibleTriangles-5923.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_12.flv">Download Link</a> <a href="/content/id/6835/Yates-Plug.flv">Download Link</a> <a href="/content/id/7511/Clip%203%20Polyplugrectangles.flv">Download Link</a> <a href="/content/id/%205974/FlashVideo.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_13.flv">Download Link</a> <a href="/content/id/6926/Stage3Final.flv">Download Link</a> <a href="/content/id/7511/Clip4%20Polyplugrectangles.flv">Download Link</a> <a href="/content/id/%206073/Always2.flv">Download
Link</a> <a href="/content/id/6307/AutoScreenRecorder_14.flv">Download Link</a> <a href="/content/id/6926/TeacherIntro3.flv">Download Link</a> <a href="/content/id/7511/Clip5%20Polyplugrectangles.flv">Download Link</a> <a href="/content/id/%206073/SumsOfSquares.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_15.flv">Download Link</a> <a href="/content/id/6927/Video.flv">Download Link</a> <a href="/content/id/7511/Clip6%20Polyplugrectangles.flv">Download Link</a> <a href="/content/id/%206073/systemspk.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_16.flv">Download Link</a> <a href="/content/id/6928/Video.flv">Download Link</a> <a href="/content/id/8260/FlashVideo.flv">Download Link</a> <a href="/content/id/%206276/GalleyDivision1.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_17.flv">Download Link</a> <a href="/content/id/6929/Stage3Final.flv">Download Link</a> <a href="/content/id/%206276/GalleyDivision2.flv">Download Link</a> <a href="/content/id/6307/AutoScreenRecorder_18.flv">Download Link</a> <a href="/content/id/6929/TeacherIntro3.flv">Download Link</a></p></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<h3>Why do this problem?</h3>
This problem gives the simplest introduction into logic gates and
circuits. Through experimentation with switches, students will
begin to see the structure of logic gates emerge without the need
for any detailed formalism. They will then see that logic gate
circuits can be constructed with more complicated behaviour. <br></br>
<h3>Possible approach</h3>
<div>Put the problem on to the board. Encourage students to read
the problem and decide what the circuit board means. Encourage
experimentation with combinations of off /off. At each stage,
encourage students to describe what they can see. How can this
sensibly be recorded?</div>
<br></br>
<div>Once students feel that they understand how a gate works they
should write a sentence describing the action of the gate. Do
others agree that this is a clear definition? How might is be
improved? Could we use it in the definition of the behaviour of the
other gates?</div>
<br></br>
<div>You might like to discuss with the class how the words 'and'
'or' and 'not' are used in real life. How does this relate to
logic-speak? Students might enjoy inventing logic-speak sentences
such as:</div>
<br></br>
<div>'I really like eating ice cream XOR chicken curry' (meaning I
like ice cream and curry, but not at the same time)</div>
<div>'I like tea XNOR milk' (meaning I only like tea with
milk)</div>
<h3>Key questions</h3>
<ul>
<li>Describe what you see.</li>
<li>What are we supposed to change? What are we supposed to leave
fixed?</li>
<li>How might we record our findings?</li>
<li>What happens if the switches in the two pairs of circuits are
set to the same values?</li>
</ul>
<div>Once students feel that they have described the gates clearly
using English, usethis follow up</div>
<ul>
<li>How could you represent the behaviour of the gate
symbolically?</li>
</ul>
<br></br>
<h3>Possible extension</h3>
<div>Once the concept of the gate is understood there are several
follow up questions, such as <a href="http://nrich.maths.org/public/viewer.php?obj_id=5973&part=">Simple
Counting Machine</a> .</div>
<br></br>
<h3>Possible support</h3>
You might suggest focussing on the AND, OR and NOT gates to begin
with<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">re<a href="/content/id/5974/Circuits_Scene%201.swf">sourc</a>e<br></br></mdoxml>
2
3
0
1
1
1
1
Clone of Circuit maker
Investigate how logic gates work in circuits.
Information and Communications Technology
Programming