You have to produce a 6-input NAND Logic Gate. But You only have 2-input NAND Gates?

Discussion in 'The Projects Forum' started by brightjoey, Nov 24, 2009.

  1. brightjoey

    Thread Starter New Member

    Nov 12, 2009
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    0
    This is a weird question from my test today. Most of my friends couldn't figure it out either.

    You have to produce a 6-input NAND Logic Gate Circuit. But you only have an unlimited number of 2-input NAND Logic Gate. Draw out the circuit design for the 6-input NAND Logic Gate.
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,135
    1,786
    You cascade the two input gates in such a way that the output is what you want it to be. A NAND gate with both inputs connected to the same source forms an inverter, aka a NOT gate.
     
  3. brightjoey

    Thread Starter New Member

    Nov 12, 2009
    14
    0
    Oh before we go any futher is this the expected output for a 6-input NAND Gate?

    F=\overline{ABCDEF}

    where A= input 1
    B= input 2
    C= input 3
    and so on..
     
    Last edited: Nov 24, 2009
  4. Papabravo

    Expert

    Feb 24, 2006
    10,135
    1,786
    Yes it is. You can also use DeMorgans Law and create an equivalent expression using NOT and OR functions
     
  5. dsp_redux

    Active Member

    Apr 11, 2009
    182
    5
    I know it's been about one month this has been posted, but since the solution has not been mentionned and the test is probably over (and the fact that I like doing this), here is the solution.
    \begin{align}<br />
F&=\overline{ABCDEF}\\<br />
&= \overline{A} + \overline{B} + \overline{C} + \overline{D} + \overline{E} + \overline{F}\\<br />
&= \overline{AB} + \overline{CD} + \overline{EF}\\<br />
&= (\overline{AB} + \overline{CD}) + \overline{EF}\end{align}<br />
    We also know that X+Y = \overline{\overline{XX}\overline{YY}}. So you'll have:
    <br />
\begin{align}<br />
\overline{AB} &= Q_1\\<br />
\overline{CD} &= Q_2\\<br />
\overline{EF} &= Q_3\\<br />
\overline{Q_1Q_1} &= N_1\\<br />
\overline{Q_2Q_2} &= N_2\\<br />
\overline{N_1N_2} &= K_1\\<br />
\overline{K_1K_1} &= K_2\\<br />
\overline{Q_3Q_3} &= K_3\\<br />
\overline{K_2K_3} &= F\end{align}
     
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