document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254834>Question 254834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how would you design a circuit for ahall light that has switches at both ends of hall such that the light can be turned on or off from either switch. I have to use this problem for this question Electrical circuits are designed using truth tables.circuit consists of switches. And wired in series as p^q. two switches wired in parallel can be use as p v q. Can you show me how to do this problem using the truth table </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187167 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a diagram of your switch could look like this:\r<BR>\n" );
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document.write( "                      A1                             A2\r\n" );
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document.write( "battery xxxxxxxxxxxxxxx  C1                      C2  xxxx light xxxxx ground\r\n" );
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document.write( "                      B1                             B2\r\n" );
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document.write( "you have battery coming in from the left going through the switches and then through the light and then to ground.\r<BR>\n" );
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document.write( "the following connections are possible through switch 1 and switch 2.\r<BR>\n" );
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document.write( "                       switch 1              switch 2           light\r\n" );
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document.write( "                       C1 to A1              C2 to A2             ON\r\n" );
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document.write( "                       C1 to A1              C2 to B2             OFF\r\n" );
document.write( "                       \r\n" );
document.write( "                       C1 to B1              C2 to B2             ON\r\n" );
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document.write( "                       C1 to B1              C2 to A2             OFF\r\n" );
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document.write( "if we let:\r<BR>\n" );
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document.write( "C1 to A1 = UP<BR>\n" );
document.write( "C1 to B1 = DOWN<BR>\n" );
document.write( "C2 to A2 = UP<BR>\n" );
document.write( "C2 to B2 = DOWN\r<BR>\n" );
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document.write( "then the table becomes:\r<BR>\n" );
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document.write( "                       switch 1              switch 2           light\r\n" );
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document.write( "                       UP                    UP                   ON\r\n" );
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document.write( "                       UP                    DOWN                 OFF\r\n" );
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document.write( "                       DOWN                  DOWN                 ON\r\n" );
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document.write( "                       DOWN                  UP                   OFF\r\n" );
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document.write( "this becomes the basis for your truth table.\r<BR>\n" );
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document.write( "in order to construct the truth tables, we will have 4 variables.\r<BR>\n" );
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document.write( "they will be U1, U2, D1, D2\r<BR>\n" );
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document.write( "U1 means switch 1 is up.<BR>\n" );
document.write( "U2 means switch 2 is up.<BR>\n" );
document.write( "U3 means switch 3 is down.<BR>\n" );
document.write( "U4 means switch 4 is down.\r<BR>\n" );
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document.write( "T means True means the switch is as indicated.<BR>\n" );
document.write( "F means False means the switch is not as indicated.\r<BR>\n" );
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document.write( "the 5th column will be L representing the light.\r<BR>\n" );
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document.write( "T means True means the light is on.<BR>\n" );
document.write( "F means False means the light is off.\r<BR>\n" );
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document.write( "Here's what your truth table would look like if constructed this way.\r<BR>\n" );
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document.write( "                        U1  D1  U2  D2  L\r\n" );
document.write( "                        T   F   T   F   T\r\n" );
document.write( "                        T   F   F   T   F\r\n" );
document.write( "                        F   T   F   T   T\r\n" );
document.write( "                        F   T   T   F   F\r\n" );
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document.write( "if the implication is that when a switch is not in the up position, then it has to be in the down position, we can simplify the truth table to be as follows:\r<BR>\n" );
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document.write( "                        U1  U2  L\r\n" );
document.write( "                        T   T   T\r\n" );
document.write( "                        T   F   F\r\n" );
document.write( "                        F   F   T\r\n" );
document.write( "                        F   T   F\r\n" );
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document.write( "U1 being true means that switch 1 is in the up position.<BR>\n" );
document.write( "U1 being false means that switch 1 is in the down position.\r<BR>\n" );
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document.write( "Similarly for U2\r<BR>\n" );
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document.write( "the logic statements for this truth table would look like:\r<BR>\n" );
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document.write( "U1 & U2 => L\r<BR>\n" );
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document.write( "this means that the state of U1 and the state of U2 both define the state of L.\r<BR>\n" );
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document.write( "Hopefully this is what you are looking for, or at least something similar to it.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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