questions about logic gates (EE, ECE, CE majors please)

[psycobreed]

is there a type of logic gate that can be used exclusively to implement any design? if yes or no, please explain why.

 

[SoylentGreen]

e=mc2

 

[Marshallj]

Why would you want to use just one kind when there are different types to choose from?

 

[brxndxn]

NAND or NOR

 

[Syringer]

Originally posted by: Kiyup
e=mc2

that's e=mc²

 

[Marshallj]

Originally posted by: psycobreed
is there a type of logic gate that can be used exclusively to implement any design? if yes or no, please explain why.

If the gate is inverting, all logic functions can be handled by one type of gate (NAND, NOR)

 

[Imaginer]

I think it maybe the nand or nor gates. With just nand gates, you can use just those instead of a circuit with and or or gates because it would be essentially cheaper to do the entire thing in one gate with programmed connections instead of remaking a chip with and and or gates.

 

[gopunk]

nand and nors can both do the job

i don't know the formal proof tho.... i just know that is the case.

 

[jaeger66]

Here is a good diagram of why NAND is universal. And god how I hated this class. Whoever invented hex should be shot. If he's dead, dug up and shot.

 

[maverik]

of course they are all right, NAND and NOR can do the job

on the more practical side, if you have a bigger circuit with ANDs and ORs, the easy way to convert it is as follows.

a NAND is and AND followed by a NOT, alternatively, by the DeMorgan's theorem, it is also NOTs followed by a single OR.
so in a circuit, put double inversions between any two gates (AND or OR gates) and then group the inversions forward and backward with the original gates. that is, lets say you have

Lets say you have an AND-OR circuit, insert NOTs after the output of every AND, and before the input of the ORs
Now you can group the first set of AND -- NOT -- as NANDs, and the NOT --OR becomes another NAND

so (A.B)+(C.D)+E is also (A NAND B) NAND (C NAND D) NAND (E NAND E)

phew, sorry for the lecture, but i got started and couldn't stop myself.

 

[gunblade]

Originally posted by: maverik
of course they are all right, NAND and NOR can do the job

on the more practical side, if you have a bigger circuit with ANDs and ORs, the easy way to convert it is as follows.

a NAND is and AND followed by a NOT, alternatively, by the DeMorgan's theorem, it is also NOTs followed by a single OR.
so in a circuit, put double inversions between any two gates (AND or OR gates) and then group the inversions forward and backward with the original gates. that is, lets say you have

Lets say you have an AND-OR circuit, insert NOTs after the output of every AND, and before the input of the ORs
Now you can group the first set of AND -- NOT -- as NANDs, and the NOT --OR becomes another NAND

so (A.B)+(C.D)+E is also (A NAND B) NAND (C NAND D) NAND (E NAND E)

phew, sorry for the lecture, but i got started and couldn't stop myself.

Just basic mixed logic design ....
I think that is really entry level stuff...

 

[jaeger66]

Originally posted by: gunblade


Just basic mixed logic design ....
I think that is really entry level stuff...

It is, but IMO digital design is like calc. The first class is always the hardest, if you can get through it everything after is easier despite harder material.

 

[FeathersMcGraw]

Originally posted by: jaeger66
Whoever invented hex should be shot. If he's dead, dug up and shot.

No one says you have to use hexadecimal as your base system. Feel free to use binary if you think it's more compact and less error-prone -- oh, but wait, it isn't.

 

[Analog]

Originally posted by: gopunk
nand and nors can both do the job

i don't know the formal proof tho.... i just know that is the case.

^

 

[kag]

Ahhh

I'm glad I'm done with my Digital Design classes. And my Assembly class too (taught by the same teacher). Oh, the microprocessor architecture too while I'm ranting

 

[KC5AV]

Originally posted by: maverik

a NAND is and AND followed by a NOT, alternatively, by the DeMorgan's theorem, it is also NOTs followed by a single OR.

NOOOOOOO!!!!!!!!!!!!!!!!!!!! Run away!!!!!!!!!!!!!!!!!!!!111

 

[etalns]

Originally posted by: Kiyup
e=mc2

of course