I'm studying logic gates, and I'm able to solve some of the expressions but not this one, and I've to submit my assignment tomorrow so please if you can help me.What does it mean to multiply a Boolean expression by 2.152?
What is it you are looking for? Someone to do your work for you?
Why? On what basis? Would we treat 0.01 as a constant TRUE? How about 0.95? Or 1.05? Or 94.3?I imagine you'd treat 2.152 as a constant TRUE or HIGH value.
That it's a very big assumption. Boolean algebra has no meaning for something like 2.152, unless that is being mapped into true, or false, as one of the two possible states, and that needs to be explicitly stated before any real meaning can be made of it.anything over 0 is considered a 1. Negative numbers would be a little trickier...
If we assume anything over 0 is a 1, and 0's remain 0s, then boolean algebra actually works out.
That's the thing, the numbers ARE being mapped to TRUE or FALSE. If the number is >0, it's TRUE, and if the number = 0, it's FALSE.That it's a very big assumption. Boolean algebra has no meaning for something like 2.152, unless that is being mapped into true, or false, as one of the two possible states, and that needs to be explicitly stated before any real meaning can be made of it.
But you are invoking a convention that is outside of Boolean algebra and it is not universal. And notice the additional caveats you had to put on it, namely that if we are adding only positive numbers. Well, what prevents us from adding a positive and a negative number? In addition, this is not even an integer, but a fractional number. And keep in mind that not all floating point representations are even capable of exactly representing zero to begin with.That's the thing, the numbers ARE being mapped to TRUE or FALSE. If the number is >0, it's TRUE, and if the number = 0, it's FALSE.
If you multiply anything by 0, you get 0, and if you multiply any two positive numbers, you get a positive number. Just like the AND function.
If you are adding only positive numbers and 0's, if any of those numbers are positive, the output is positive. Just like the OR function.
This is why we use the symbols we use for AND and OR functions. This is the thought process and mathematical model/reasoning George Boole used to develop boolean algebra in the first place.
You simply can't use negative numbers, as far as I can tell.But you are invoking a convention that is outside of Boolean algebra and it is not universal. And notice the additional caveats you had to put on it, namely that if we are adding only positive numbers. Well, what prevents us from adding a positive and a negative number? In addition, this is not even an integer, but a fractional number. And keep in mind that not all floating point representations are even capable of exactly representing zero to begin with.
If it has nothing to do with the representation of numbers to work, and if they don't even have to be integers for it to work, then why won't it work with negative numbers?You simply can't use negative numbers, as far as I can tell.
The numbers don't have to be integers for this to work.
This has nothing to to with floating point numbers, or representation of numbers within' a computer at all. This is simply mathematical theory.
So please show how it works with XOR?a(b+c) = ab + ac in boolean algebra.
Write out the truth table for this expression. You'll find that if you replace HIGH/1 with any positive number, and you do the math with ordinary algebra, and find the solution, every time the output should be 0, it will be 0, and any time the output should be HIGH/1, the answer will be a positive number.
Basically, it DOES work.
I'm still unsure if you could find a way to get negative numbers to work though. That, and I'm not sure if there's a function, using regular algebra, that will perform the boolean inverse function.
It's just an observation I made early on, and I suspect the idea went into the forming of boolean algebra to some extent.
So please show how it works with XOR?
If it doesn't, then the whole notion is bushwah.
It was just a curiosity, really. Boolean algebra and ordinary algebra share certain characteristics. In fact, I'm looking and wondering if there's a way to perform boolean algebra entirely using ordinary algebraic rules. Basically, find algebraic functions that perform the boolean algebraic functions.But what is !B.
Your whole premise seems to be that we can mix and match non-negative values and Boolean logic values as we wish and just reduce things at the end.
So if I have A=3.4 and B=2.1, you are saying this is okay because we can multiply 3.4 by 2.1 and THEN convert them to True and False. Okay, so what is A+!B using the values before converting to True or False. If we have to convert before combining, then we could define ANY set of values (or even symbols) to be True and some other set to be False and be right in the same position.
Where was this stated in the OP? Why is it mapped that way? Who said?That's the thing, the numbers ARE being mapped to TRUE or FALSE. If the number is >0, it's TRUE, and if the number = 0, it's FALSE.[...]
Where was this stated in the OP? Why is it mapped that way? Who said?
You can't just come in and claim that this is what is going on without being told that this is the mapping.
Anything else is just an assumption.