AND-OR to NAND-NAND

1. Feb 13, 2010

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

2. Feb 14, 2010

awelex

Nobody?

3. Feb 15, 2010

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.

Last edited: Feb 15, 2010
4. Feb 16, 2010

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.