| ??? 07/04/03 05:04 Read: times |
#50043 - Bubbles Responding to: ???'s previous message |
I have a 'serious problem ' with you - none of your posts can be read on the fly and the idea grasped!!
I aplologize... {grin} Well, it's not so easy to decide how much to write. I could drastically decrease number of words, but then you would reply: 'What do you mean with...'. Or others would state: 'No, no, there are too many guesse and assumptions...' When I was much younger, I was often angry with textbook writers, not to go into more detail. So, there were always some doubts left, after reading a chapter. The bubble stuff was confusing to me 20 years back. Should say things ( I ) have not changed one bit ! The reason for the bubbles is just mathematics. Behind mechansims of truth table there is lots of mathematics. There's one interesting point, which can be derived from theory: It's possible to represent every static truth table by a circuit consisting of only NAND gates. So, if you have only 7400 devices (tons of them), you can solve every imaginable static truth table. Isn't this amazing? The same is true: You can solve every imaginable static truth table by a circuit consisting of only NOR gates. Of course, it would be stupid to realize complex gate circuitry by the help of only NAND or NOR gates, because you would need much more gates than when just using the complex ones, like EXOR etc., but from a theoretical point of view it's possible. And between NAND gates and NOR gates there is a special relationship, which is expressed by the de-Morgan theorem. And it's just this theorem which needs the bubbles. There's a very simple rule of thumb which helps to keep in mind de-Morgan theorem: Imagine you want to know, how a NAND gate looks like in NOR technology and vice versa, then do the following: 1. Make a bubble (means inversion of according signal) at every input and ouput. 2. Transform AND symbol to OR or vice versa. This gives you the equivalent, by just applying de-Morgan theorem. So, you see, these bubbles are very helpful... Bye, Kai |



