OR AND gates as a basis for more gates?

[neazoi]

Hello I have read somewhere that from OR and AND gates, all the other gates can be made. Is there any page that explains how to build all the other gates from these two types?

 

[permute]

you have it wrong, its NAND gate or NOR gates. both NAND gate and NOR gates can form any other 2 input logic function. eg, if you only have NAND gates, you can make any other logic function.

AND/OR cannot do this, as there is no inverter.

keep in mind that multiple levels of NAND gates might be required.

example of an AND gate made from NAND.
x and y = not x nand not y = (x nand x) nand (y nand y)

and this is generally the idea for the rest of the gates.

 

[neazoi]

Thank you,
Is there any site that could practically explain the creation of the additional gates from basic ones?

 

[loopaloopa]

yeah, NAND and NOR gates are the universal gates.. so the two gates can function as the basic logic gates and coincidence gates.... the book of DIGITAL DESIGN by MORRIS MANO has the equivalent circuit of NAND and NOR for the OR, AND and NOT gates.... its the NAND and NOR gate implementation...

 

[neazoi]

yeah, NAND and NOR gates are the universal gates.. so the two gates can function as the basic logic gates and coincidence gates.... the book of DIGITAL DESIGN by MORRIS MANO has the equivalent circuit of NAND and NOR for the OR, AND and NOT gates.... its the NAND and NOR gate implementation...

Actually a NOR can be derived from NAND too

 

[alaparthi]

Though NOR Gate is realizable from NAND, Both NAND and NOR are required and considered as Universal Gates because, when you look at the Corresponding CMOS Circuits, these two can be available with out extra inverting operation and minimum number of transistors.

Suppose, 2input NAND Gate:

2NMOS in Series and 2PMOS in Parallel.

Similarly, 2 input NOR Gate:
2PMOS in Series and 2NMOS in Parallel.

That is why, people prefer to realize all circuits using these two as building blocks.