is the following a legitimate way to create an xor gate?


simulate this circuit – Schematic created using CircuitLab

The AND with the two NOT inputs would be a NOR, but I'm seeing with just two gates -- AND + NOT -- if the below is a valid way to build an XOR gate or if I'm missing something. The above would eventually decompose into:


simulate this circuit


1 Answer 1


Yes, that's a legitimate way with AND gates.

NAND or NOR gates are usually the primitives available so an XOR would be built from those in practice.

  • \$\begingroup\$ thanks. Could you please explain what you mean by "primitives" ? Why wouldn't the three basic gates be and/or/not, since those would be the most basic? \$\endgroup\$
    – David542
    Mar 22, 2020 at 20:46
  • 5
    \$\begingroup\$ @David542 The availability of gates reflects the underlying electronic elements that are used to construct them. It so happens that NOR/NAND require less transistors to realize in typical processes/logic families such as CMOS, even though they aren't as "basic" from a purely logic analysis/design standpoint. \$\endgroup\$
    – nanofarad
    Mar 22, 2020 at 20:51
  • 2
    \$\begingroup\$ Hi David, NAND and NOR gates are primitives cuz they both can easily be produced from CMOS , this link explains fundementals-> vlsifacts.com/nand-gate-using-cmos-technology. \$\endgroup\$
    – emre iris
    Mar 22, 2020 at 20:52
  • 1
    \$\begingroup\$ It is also possible to reconstruct all possible logic gates just using several 2 input NAND or NOR gates. \$\endgroup\$
    – Grabul
    Dec 5, 2022 at 20:07

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