1 Attachment(s)

Boolean Algebra Truth Table for fundamental conjunction and dnf

Attachment 28925

Hello again! Can anyone help me understand how f, g and h got their column of answers from xyz columns? Is it thru multiplication or addition?

Thanks.

i would appreciate it if the explanation is in simple english, i am very poor with mathematical symbols. Need to

understand this before i could move on with my assignment.

I would understand the truth table if the examplr gave an expression like xy+z, then I'd solve for that because i'll know what to multiply and what to add. But the example above is just looking for fundamental conjunctions with a value of 1 and i don't know how f g h got their 1's and 0's.

Thanks again!

Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

The functions f, g and h are just given. The fundamental idea of a function is that it is some way of converting an input into an output. Writing an expression with "and", "or" and "not" is just one way to define a Boolean function. We can use any means as long as it guarantees that every possible input is connected to a single output. In this case, f, g and h are given by explicitly listing their values for each input. The text says, "Let's consider these particular functions". Now, it turns out that every Boolean function can be specified by a Boolean expression, as in this example. This is not the case for functions on real numbers or even natural numbers. For example, the function that, given the coefficients a_{4}, ..., a_{0} of a polynomial x^{5} + a_{4}x^{4} + ... + a_{0} of degree 5 returns the smallest root of this polynomial cannot be expressed using the four arithmetical operations and roots.

Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

So.... xyz was not calculated to get f and g all along? the textbook just put jumbled 0's and 1's on the f and g column with no calculation? and f(xyz)= ~x~yz =1 is also a given and I have to look into the table which is negatable in that way?

hehe thanks :)

2 Attachment(s)

Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

I have to understand the example for me to be able to answer my assignment problems 4 and 5. Your explanation is waaaaay better than my instructor's:

Indeed.

Looking at one line... to explain....

the second line has the values of x=0, y=0 and z=1

in the explanation ... the function f is = x'y'z = x'*y'*z

>> the terms are multiplied to gether

the value of x' is 1

the value of y' is 1

the value of z is 1

so the result of f = x'y'z = 1*1*1 = 1

It would seem that you are not seeing how the functions f and g and h are described in the write up.

Look clearly into the values of the functions...

onward

He didn't say that f values are given already. He just "rephrased" the example. Which I still don't get it, and yes he explains like that too, like a robot. It drives me crazy haha

This is my assignment by the way:

Attachment 28927

This is what I did (don't mind the note I have on the bottom part, that's what I asked my professor again and again):

Attachment 28928

Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

So with my work uploaded, with w=x=0, y=z=1 given, I will automatically make put 1 on the f column where I see w=0, x=0, y=1, z=1, but then all zeros on other rows of f, right? Am i on the right track?

Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

When you said f is given, it gave me light!

So what this guy is saying makes sense to me now:

From Truth Table to DNF or CNF - YouTube

From Truth Table to DNF - YouTube

Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

Quote:

Originally Posted by

**jpab29** i have to understand the example for me to be able to answer my assignment problems 4 and 5. Your explanation is waaaaay better than my instructor's:

indeed.

Looking at one line... To explain....

The second line has the values of x=0, y=0 and z=1

in the explanation ... The function f is = x'y'z = x'*y'*z

>> the terms are multiplied to gether

the value of x' is 1

the value of y' is 1

the value of z is 1

so the result of f = x'y'z = 1*1*1 = 1

it would seem that you are not seeing how the functions f and g and h are described in the write up.

Look clearly into the values of the functions...

Onward
he didn't say that f values are given already. He just "rephrased" the example. Which i still don't get it, and yes he explains like that too, like a robot. It drives me crazy haha

this is my assignment by the way:

Attachment 28927
this is what i did (don't mind the note i have on the bottom part, that's what i asked my professor again and again):

Attachment 28928

wait!!! My truth table is wrong! Lol hahaha

i'll redo it. :)

w 1-8 should be 0 and 9-16 should be 1... And so the other columns i will redo. So sorry. Gosh i'm math drunk. :)

Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

on second thought, I thought I got it wrong. hehehe It was my other assignment.

emakarov, thank you so much for your help. My grades in math are actually dangerously failing, and week 5 (this last week) was my last chance. When I get the results back (hopefully I pass), I will post the answers I had here as help for future students who need.

Thanks again!