title: Essential Prime Implicants and Minterm Expressions
body: <p>I have an exam for a university course shortly, and upon reviewing one of my assignments I have come to realize that I don't understand why I have lost marks/how to do a couple of questions. Hopefully someone can shed some light on the subject for me! The questions were as follows:</p>
  
  <p>Use K-Maps to simplify the following boolean functions (Note that d() represents a don't care minterm):</p>
  
  <p>1.) F(w, x, y, z) = ∑(1,3,5,7,11,12,13,15)</p>
  
  <pre><code>My answer:
  Prime Implicants: yz, w'z, xz, wxy'
  Essential Prime Implicants: yz, w'z, wxy'
  Possible Minimal Expression(s): yz + w'z + wxy'
  
  Answer sheet (professor's answer):
  Prime Implicants: yz, w'z, xz, wxy'
  Essential Prime Implicants: Same as prime implicants
  Possible Minimal Expression(s): yz + w'z + xz + wxy'
  </code></pre>
  
  <p>2.) F(w, x, y, z) = ∑(1,2,5,7,12) + d(0,9,13)</p>
  
  <pre><code>My answer:
  Prime Implicants: w'x'z', y'z, w'xz, wxy', w'x'y'
  Essential Prime Implicants: w'x'z', w'xz, wxy'
  Possible Minimal Expression(s): w'x'z' + w'xz + wxy'
  
  Answer sheet (professor's answer):
  Prime Implicants: w'x'z', y'z, w'xz, wxy', w'x'y'
  Essential Prime Implicants: w'x'z', w'xz, wxy'
  Possible Minimal Expression(s): w'x'z' + w'xz + wxy' + y'z
  </code></pre>
  
  <p>I suppose I should add that I asked my professor after he returned my assignment to me if he had made a mistake and explained my point of view. He seemed pretty certain that he was correct, but couldn't really explain why because he speaks poor English (well, that's university for you..).</p>
  
  <p>Thanks in advance to anyone who can help! This has been quite a task to try to figure out on my own!</p>