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    <div class="moz-cite-prefix"><br>
      I think you would count every operator as a gate if you were to
      realize this with discrete logic.  So five, I suppose.<br>
      <br>
      Clif, is this the same "three-gate, two with inverting input" you
      described?<br>
      <br>
      On 1/16/2014 9:19 AM, Mark Danburg-Wyld wrote:<br>
    </div>
    <blockquote
cite="mid:CAAFW7yic-jQ0B2vCbf_KfAkf6hKNYc+-w+vZsCoV+eoCO5my9g@mail.gmail.com"
      type="cite">
      <div dir="ltr">
        <div>I don't know what constitutes a gate, but I do know my
          symbolic logic...<br>
          >>> def outputs(a, b):<br>
              c = a & b<br>
              d = a & ~c<br>
              e = b & ~c<br>
              print c, d, e<br>
              <br>
          >>> outputs(0, 0)<br>
          0 0 0<br>
          >>> outputs(0, 1)<br>
          0 0 1<br>
          >>> outputs(1, 0)<br>
          0 1 0<br>
          >>> outputs(1, 1)<br>
          1 0 0<br>
          >>> <br>
          <br>
        </div>
        So is that 3 gates, or 5?<br>
      </div>
      <div class="gmail_extra">
        <br>
        <br>
        <div class="gmail_quote">On Thu, Jan 16, 2014 at 8:58 AM, Mr.
          Clif <span dir="ltr"><<a moz-do-not-send="true"
              href="mailto:clif@eugeneweb.com" target="_blank">clif@eugeneweb.com</a>></span>
          wrote:<br>
          <blockquote class="gmail_quote" style="margin:0 0 0
            .8ex;border-left:1px #ccc solid;padding-left:1ex">
            <div bgcolor="#FFFFFF" text="#000000"> Way to go Darrell!<br>
              <br>
              That sounds perfectly normal except that if I understand
              you correctly you would say that the output of the AND
              gate propagates into the inputs of the XORs.<br>
              <br>
              After I went to bed last night I realized that with the
              MC10H104 I can also do it with three of the four gates in
              just that one package. So not only can I do it in three
              gates I can also do it without buying several different
              gate packages.<br>
              <br>
              Ok Weston you've got two guys that claim to have solved it
              in three gates! :-p what now?<span class="HOEnZb"><font
                  color="#888888"><br>
                  <br>
                      Clif</font></span>
              <div>
                <div class="h5"><br>
                  <br>
                  <div>On 01/16/2014 03:21 AM, Darrell Perko wrote:<br>
                  </div>
                  <blockquote type="cite">
                    <div><br>
                      I think I have a solution using two XOR and one
                      AND, though the AND is both an output and it feeds
                      back into the input of the XORs.  That seems like
                      it could cause brief illegal outputs states.<br>
                      <br>
                      On 1/15/2014 11:49 PM, Mr. Clif wrote:<br>
                    </div>
                    <blockquote type="cite"> Ok here is a Quad and gate
                      part that you can do it with just one package:<br>
                      <br>
                      MC10H104<br>
                      <br>
                      there may be others.<br>
                      <br>
                          Clif<br>
                      <br>
                      <div>On 01/15/2014 10:40 PM, Mr. Clif wrote:<br>
                      </div>
                      <blockquote type="cite"> Ok ;-)<br>
                        <br>
                        So when you say that "<span
                          style="font-family:courier new,monospace"><font
                            face="arial,helvetica,sans-serif"><span
                              style="font-family:courier new,monospace"><font
                                face="arial,helvetica,sans-serif">inverting
                                operations count as NOT gates</font></span></font></span>"
                        do you mean that they aren't counted as gates or
                        that they are "Not operations"  implemented as
                        gates, which of course they are?<br>
                        <br>
                        One issue with doing this your way in hardware,
                        is that you need three different types of gates
                        unless you are doing it in an FPGA or the like.<br>
                        <br>
                        Here it is in a shorter logical expression:<br>
                        <span style="font-family:courier new,monospace">C
                          = <span
                            style="background-color:rgb(255,242,204)">A
                            & B</span>; D = <span
                            style="background-color:rgb(217,234,211)">!C
                            & A</span>; E = <span
                            style="background-color:rgb(207,226,243)">!C
                            & B</span></span><br>
                        <br>
                        I have another way that uses four of the same
                        kind of gate though they may be some what
                        uncommon. ;-)<br>
                        <br>
                            Ciao,<br>
                            Clif<br>
                        <br>
                        <div>On 01/15/2014 10:04 PM, Weston Turner
                          wrote:<br>
                        </div>
                        <blockquote type="cite">
                          <div dir="ltr">
                            <div><span style="font-family:courier
                                new,monospace"><font
                                  face="arial,helvetica,sans-serif"><span
                                    style="font-family:courier
                                    new,monospace"><font
                                      face="arial,helvetica,sans-serif">From
                                      a more rigorous or theoretical
                                      standpoint, the inverting
                                      operations count as NOT gates</font></span>.
                                  But I guess I didn't say that
                                  inverting equals a NOT. In any case,
                                  my four gate solution doesn't use
                                  them. I'll represent it here in Python
                                  using four binary bitwise operators,
                                  one AND, one OR, and two XORs. <br>
                                  <br>
                                  A and B are anded to make C<br>
                                  A and B are ored  together into the
                                  temp variable t<br>
                                  t is xored with B to make D<br>
                                  t is xored with A to make E<br>
                                  <br>
                                </font></span></div>
                            <div><span style="font-family:courier
                                new,monospace"><font
                                  face="arial,helvetica,sans-serif">The
                                  operations are color coded below. Can
                                  this be done with fewer operations?<br>
                                </font></span></div>
                            <div><span style="font-family:courier
                                new,monospace"><br>
                                Python 2.7.3 (default, Nov 11 2012,
                                18:06:39) <br>
                                >>> <b>A, B = 0, 0</b><br>
                                >>> t = <span
                                  style="background-color:rgb(244,204,204)">A
                                  | B</span>; C = <span
                                  style="background-color:rgb(255,242,204)">A
                                  & B</span>; D = <span
                                  style="background-color:rgb(217,234,211)">B
                                  ^ t</span>; E = <span
                                  style="background-color:rgb(207,226,243)">A
                                  ^ t</span><br>
                                >>> C, D, E<br>
                                <b>(0, 0, 0)</b><br>
                                >>> <b>A, B = 0, 1</b><br>
                                >>> t = A | B; C = A & B; D
                                = B ^ t; E = A ^ t<br>
                                >>> C, D, E<br>
                                <b>(0, 0, 1)</b><br>
                                >>> <b>A, B = 1, 0</b><br>
                                >>> t = A | B; C = A & B; D
                                = B ^ t; E = A ^ t<br>
                                >>> C, D, E<br>
                                <b>(0, 1, 0)</b><br>
                                >>> <b>A, B = 1, 1</b><br>
                                >>> t = A | B; C = A & B; D
                                = B ^ t; E = A ^ t<br>
                                >>> C, D, E<br>
                                <b>(1, 0, 0)</b></span><br>
                              <br>
                            </div>
                            <div>Cheers,<br>
                            </div>
                            <div>Weston<br>
                            </div>
                            <br>
                          </div>
                          <div class="gmail_extra"><br>
                            <br>
                            <div class="gmail_quote">On Wed, Jan 15,
                              2014 at 8:42 PM, Mr. Clif <span dir="ltr"><<a
                                  moz-do-not-send="true"
                                  href="mailto:clif@eugeneweb.com"
                                  target="_blank">clif@eugeneweb.com</a>></span>
                              wrote:<br>
                              <blockquote class="gmail_quote"
                                style="margin:0 0 0 .8ex;border-left:1px
                                #ccc solid;padding-left:1ex">Sure I can
                                do it in three but two of the gates have
                                to have one inverting input each. Since
                                gates often come in quad packs it might
                                be nice to find a circuit that would use
                                all four in a pack. Though if it helps
                                my fourth gate is just an inverter and
                                there are often left over ones from
                                other packages.<br>
                                <br>
                                    Clif
                                <div>
                                  <div><br>
                                    <br>
                                    <br>
                                    <br>
                                    <br>
                                    On 01/15/2014 07:42 PM, Weston
                                    Turner wrote:<br>
                                  </div>
                                </div>
                                <blockquote class="gmail_quote"
                                  style="margin:0 0 0
                                  .8ex;border-left:1px #ccc
                                  solid;padding-left:1ex">
                                  <div>
                                    <div> I'm wondering if anyone can
                                      implement this logic table with
                                      less than four gates...<br>
                                      <br>
                                      A B | C D E<br>
                                      -------------<br>
                                      0 0 | 0 0 0<br>
                                      0 1 | 0 0 1<br>
                                      1 0 | 0 1 0<br>
                                      1 1 | 1 0 0<br>
                                      <br>
                                      I figured out a way to implement
                                      it with four gates but I'm
                                      wondering if it can be reduced
                                      further...<br>
                                      <br>
                                      And if you can only figure out a
                                      way to do it with four, then I'm
                                      curious to see if you arrived at
                                      the same solution I did.<br>
                                      <br>
                                      Regards,<br>
                                      Weston<br>
                                    </div>
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