NAND gates alone are universal - that is, any truth table can be implemented by a circuit that includes only NAND gates.
To convince ourselves of this, we start with the fact that any truth table can be implemented using AND, OR, and NOT gates; and then we see how one can replace each AND/OR/NOT gate with a system of NAND gates to arrive at a circuit including only NAND gates. This circuit demonstrates the NAND-gate system corresponding to each of AND, OR, and NOT.
The fact that NAND is universal is often used by circuit designers. Though designers at first design a circuit using AND, OR, and NOT gates, in practice circuits are easier to manufacture when they use only NAND gates (or only NOR gates). Thus, their initial AND/OR/NOT designs are converted to use only NANDs (or NORs).
Enjoy...😎
