basic logic question

[newbiet]

am new to digital electronics and am wondering why the logic for the output of a OR gate is equivalent to a + sign when evaluating an expression..

for example if i was drawing the circuit for the following experession F=A + B...I would use an OR gate with A and B as inputs and F as the output. Yet the truth table for an OR gate is different to that of a Sum output when using a Half Adder to add bits A and B..don't under stand this..

 

[(*steve*)]

+ is just used as a notation, it does not mean addition.

 

[poor mystic]

Hi newbiet
'OR' is not equivalent to 'plus' in any way - it is just that convention uses the same symbol for 2 quite different concepts, which can be very confusing.

 

[newbiet]

notation

So using a + for an OR gate is just poor notation.
Using a '.' for an AND makes sense though.......!?

 

[daddles]

No, it's perfectly acceptable notation and was likely invented long before any of us were alive. In programming, this is called operator overloading because there are many more operations than there are symbols on the keyboard (I exclude Unicode). You can see that it would be very clumsy to e.g. have to use a different symbol for matrix addition than to just use the + symbol. Yet adding numbers and adding matrices or vectors are completely different concepts -- and the problem becomes worse as you go into more abstract things in mathematics. Thus, it's important for an expositor to list his/her symbols and notation. However, for elementary things like Boolean algebra, it's not usually done because most folks know the details. Now you know too.

 

[poor mystic]

I don't know who invented the notation either, but I suspect it may have been St. Claude (Shannon)
https://secure.wikimedia.org/wikipedia/en/wiki/Boolean_logic

 

[daddles]

It's in Boole's "An investigation of the laws of thought" published in 1854.

 

[poor mystic]

It's in Boole's "An investigation of the laws of thought" published in 1854.

Wowee. Does Boole actually use that notation? I had assumed it was all conjunct this and disjunct that.
Oh well St Claude didn't invent everything. I guess.

 

[daddles]

Oh well St Claude didn't invent everything. I guess.

Well, his most important invention was the Dirt Claude. And his first-name namesake grandfather on his mother's side (nee Balls) wrote a book called "Tiger's Revenge".

 

[poor mystic]

daddles will have his little joke.




after a while, if we are... lucky! he will explain it.

 

[poor mystic]

If you like being confused btw i can help!
The following functions convert numbers for use in logical operations:
XOR(a,b) = (1/2)*((-1)^(a+b)+1)
AND(a,b) = (1/2)*((-1)^(ab)+1)
These functions imply a kind of logic in which XOR and not OR is a fundamental operation.
Also as you have pointed out addition and multiplication have their application as logical functions.
Best stick with Boole until after the exam.

 

[(*steve*)]

daddles will have his little joke. .

I have a feeling they may be what my wife refers to a "Dad Jokes".

Just be thankful I'm not posting any (he says, hoping nobody spots the one he posted earlier...)

 

[TBennettcc]

See number 36 on this list:

http://terhune.net/jokes/books.txt.html

"The Tiger's Revenge" by Claude ("Clawed") Balls...

And as far as the dirt reference goes,

clod:

noun /kläd/ 
clods, plural

A lump of earth or clay

Very clever, Daddles...