title: Digital Logic - truth tables
body: <p>I am trying to solve these problems with truth tables using the formulas below. I am having a problem with the NOT to NAND</p>
  
  <p>I think i got the first 2 problems correct using: AND is equivalent to NOR, AND is  equivalent to NAND</p>
  
  <p>The equations for AND, OR and NOT using the NAND operator are:</p>
  
  <pre><code>X + Y = x' NAND y' ??
  X * Y = 
  X' = X NAND 1
  </code></pre>
  
  <p>The equations for AND, OR and NOT using only the NOR operator are: </p>
  
  <pre><code>X' = ?
  X + Y = (X NOR Y) NOR 0
  X * Y = X' NOR Y' ??
  </code></pre>
  
  <p>I am trying to follow this formula</p>
  
  <pre><code>An OR gate with a NOT in both inputs is equivalent to a NAND.
  An AND gate with a NOT in both inputs is equivalent to a NOR.
  An OR gate with a NOT in its output is equivalent to a NOR.
  An AND gate with a NOT in its output is equivalent to a NAND.
  </code></pre>
  
  <p>this is how i worked out AND to NOR equivalent</p>
  
  <pre><code>X  Y    X AND Y      X NOR Y    
  -----------------------------
  0  0       0            1
  0  1       0            0
  1  0       0            0
  1  1       1            0
  
  X'  Y'   X' NOR Y'
  -------------------
  1   1        0
  1   0        0
  0   1        0
  0   0        1
  </code></pre>
  
  <p>My biggest problem is how do i use a NOT in the outputs in a truth table? Also, how would i go from a NOT to a NOR? I want to work all these out in a truth table.</p>
  
  <pre><code>X * Y = "An AND gate with a NOT in its output is equivalent to a NAND."
  </code></pre>
  
  <p>what are the outputs in a  truth table? and how can i go from a X' to equivalent NAND?</p>