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XMN(A,B,C,D)=(A XOR B) NAND (C NOR D).

Is XMN is universal operator? a. yes without constants. b. yes with 0 constant c. yes with 1 constant d. yes with OR gate. e. no.

  1. What does it means universal operator with OR gate?
  2. Is there a method without hinting variables, for example, with karno map to know if the function is universal operator?
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  • \$\begingroup\$ @jsotola This is not an assignment. That is one of a questions that I try to understand in order to be prepared for my exam in digital systems course. \$\endgroup\$ – John D Jan 22 '20 at 9:43
  • \$\begingroup\$ What is your definition of a "universal operator"? Can you show us an example of a different "universal operator"? \$\endgroup\$ – Elliot Alderson Jan 22 '20 at 12:42
  • \$\begingroup\$ @ElliotAlderson Universal operator is one that can implement any arbitrary logic function. NAND and NOR are examples. AND, XOR, and NOT aren't, since there are functions that can't be implemented using only the single function. \$\endgroup\$ – Cristobol Polychronopolis Jan 22 '20 at 13:33
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It is, because you can tie B and D low and the function is now A NAND (NOT C). Tie B, C, D low and it's an inverter, so you can make a NAND out of it, which is universal.

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  • \$\begingroup\$ Thank you! Could you please explain what does it means when function is universal with some of gates and without is not? How is it possible to check it, in general? \$\endgroup\$ – John D Jan 22 '20 at 19:42
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    \$\begingroup\$ It has to provide inversion, and it has to combine two inputs. NOT isn't universal because there's no way of combining inputs. AND and OR don't provide inversion. XOR is trickier...it's incomplete because it provides only a relative comparison (you can tell if the inputs are different, but not which is high and which low). My way to determine higher-than-binary functions is, if you can build a NAND or NOR from the function, it's universal, as I showed above. \$\endgroup\$ – Cristobol Polychronopolis Jan 22 '20 at 20:23

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