Understanding NAND-NAND Expressions: Conversion & Circuit Design

[awelex]

Hi,

I have a question about NAND-NAND expressions. I do understand the conversion from AND-OR to NAND-NAND, but what I don't understand is how many textbooks show the resulting circuit, i.e. with an OR gate with inverted inputs as the top-level gate, such as in the second circuit here:

http://cfs.tistory.com/attach/6445/259783.bmp

I know that the conversion is algebraically correct, but doesn't a NAND-NAND circuit consist only of, well, NAND gates? How can an OR gate be used, then?

Thanks

 

[awelex]

Nobody?

 

[uart]

The "OR gate with inverted inputs" is a nand (by DeMorgans Law). Some people prefer to draw it that way presumably just to make it more transparent (as in how you got from AND/OR to NAND/NAND). You see when it's drawn that way the double complements obviously cancel out (as in not(not(x)) = x), so you can see the equivalence of the two forms by simple inspection.

 

[zgozvrm]

Each of the little open circles in this type of diagram represent an inversion of the signal (a NOT, if you will). So, you can place 2 circles in series without changing anything logically.

Also, you can invert all inputs and outputs of a gate (by adding or removing circles) and then change and the type of gate from AND to OR, or vice-versa. This will also preserve the logical value of the circuit, which is why the right hand gate in the second diagram is considered to be a NAND gate.