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Lesson 0101: SOP Format and The Universal Sets

SOP format

An equation must be simplified as it is instructed in the directions, e.g. "with the least number of parenthesis" or "using the least possible number of gates". However, if nothing is mentioned, it is usually implied that the equation needs to be simplified into SOP format. SOP stands for "Sum Of Products". SOP format means that you are limited to the 3 operations, AND, OR, and NOT.

That is because those three gates together form a universal set. That means that any equation can be expressed only by using those three operators. By itself, NOR and NAND are also universal sets. Any equation taken from SOP format can be changed so that it is only formed of the gates of "NOR" and "NAND".

Check your progress

Simplify the following equations into SOP format:

  1. [not A]B+ [not (A xor B)]*[not A]

      1
      0
      not A
      not B
      A+B

  2. [A xor B] + AB+ [not(AB)]

      1
      0
      NOT(AB)
      ~A+~B

  3. [A equiv B] + [A xor B]

      1
      0
      A NAND B
      A NOR B
      A AND B
  4. [not(not(AB)+A)] + [A nor B]

      1
      0
      ~A~B
      ~(AB)
      ~A+~B


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