# Expression from truth table and simplifying boolean

#### Joeaz123

Joined Nov 19, 2016
6
Hey,
Just started up on my new logic gates module and wondering if anyone could give me a little feedback and assistance,

I got a Boolean equation to simplify

( A . B + A . B . C + A . B . C . D + A . B . C . D . E + A . B . C . D . E .F)

The . is an AND
The + is an OR

I got; A.B.C.D.E.F

Am I completely wrong or doing it right? Just wondering so in future I don't make mistakes, sorry for such a newbie question If it's wrong could anybody tell me how I would go about doing it correctly?

I got also a truth table to work out, I really have no idea how to approach the truth table, I need to work out X, though I'm not asking for anybody to do it for me, just how will I go about working it out?

#### Joeaz123

Joined Nov 19, 2016
6
Sorry for double posting but there isn't an edit option.

After more working out and going over some issues I ended up with A.B for my final simplification.
I still cannot work out what I should be doing for the truth table from notes & slides.

#### WBahn

Joined Mar 31, 2012
25,765
Your expression have six variables yet your truth table only has three. Does that make sense?

The expression you got, A.B.C.D.E.F, says that for the output to be True that all six of the inputs must be True. Is that consistent with either the original expression or the truth table you give.

One of the first things you need to start doing is always, always, ALWAYS, ask if your results make sense.

#### WBahn

Joined Mar 31, 2012
25,765
Sorry for double posting but there isn't an edit option.

After more working out and going over some issues I ended up with A.B for my final simplification.
I still cannot work out what I should be doing for the truth table from notes & slides.
That's a much more sensible result.

For the truth table, any row in which both A and B are True should have an output that is True. Your truth table should have one column for each input variable. I suspect that you are expected to realize that in four of the columns you can use all X's, meaning that the value of that variable doesn't affect the output.

#### MrChips

Joined Oct 2, 2009
21,143
How many minterms are in a six-variable truth-table for A, B, C, D, E, F?
How many of these minterms are represented by A.B?

#### Joeaz123

Joined Nov 19, 2016
6
I would hope you mean A.B is correct or am I still missing something? It's all a little confusing, I've not approached anything similar before.

The question for the truth table is just; Find the expression for X from the truth table

so if A & B are True, that means the expression I'm looking for is True (1)?

It's just a bit confusing, in all my examples, we convert the table above to look like this; After we've converted the 0s and 1s to NOT A, NOT B etc
We work out the input. The table is confusing because I don't really follow what it means, none of our tables look like that.

I don't understand if he means be to say if A B C is 1 or 0 (True, False) or he's asking should something else be there, it's weird. The question isn't very helpful either.

I thought X would be 1, but it seems awfully easy and I thought I was missing something.

#### WBahn

Joined Mar 31, 2012
25,765
Ah, I see now that you have two unrelated problems. I thought you had an expression, were simplifying it, and then coming up with the truth table for that expression. This is why we strongly encourage just one problem per thread -- it becomes chaotic otherwise as you can't tell which problem a given response is referring to.

For your second problem, this might help:

#### Joeaz123

Joined Nov 19, 2016
6
Ah, I see now that you have two unrelated problems. I thought you had an expression, were simplifying it, and then coming up with the truth table for that expression. This is why we strongly encourage just one problem per thread -- it becomes chaotic otherwise as you can't tell which problem a given response is referring to.

For your second problem, this might help:

Apologies. I did have a little look at that, it's the table layout which is confusing me, I'm not really sure what I'm actually looking for, it seems the layout is weird and unseen.

The X for the truthtable would just be a letter, such as F or G? It doesn't make sense to me, I was hoping someone could tell me what I'm looking for or what the answer is and why it's that, sorry for the confusion.

#### WBahn

Joined Mar 31, 2012
25,765
Apologies. I did have a little look at that, it's the table layout which is confusing me, I'm not really sure what I'm actually looking for, it seems the layout is weird and unseen.

The X for the truthtable would just be a letter, such as F or G? It doesn't make sense to me, I was hoping someone could tell me what I'm looking for or what the answer is and why it's that, sorry for the confusion.
I don't know what you mean by "weird and unseen", could you expand on that a bit?

In your problem, yes, X is just the output variable, so you are looking for a Boolean expression of the form

X(A,B,C) = ....

Which simply means that X is a function of the inputs A, B, and C.

#### Joeaz123

Joined Nov 19, 2016
6
I don't know what you mean by "weird and unseen", could you expand on that a bit?

In your problem, yes, X is just the output variable, so you are looking for a Boolean expression of the form

X(A,B,C) = ....

Which simply means that X is a function of the inputs A, B, and C.
That's what I first thought, I second guessed myself he wanted if ABC and if that was true or false, the only gates I've seen are from the few sessions I've had, I thought it was odd he would just want any random variable, but I understand now. I'm sorry about all this confusion, I really appreciate you taking the time to help me understand it better.

So writing this would be; (A,B,C) = D

Would this work? I'm basically just writing the equation for a variable I don't know it's value in a sense? I'm more or less saying A, or, B or C = X?

#### WBahn

Joined Mar 31, 2012
25,765
That's what I first thought, I second guessed myself he wanted if ABC and if that was true or false, the only gates I've seen are from the few sessions I've had, I thought it was odd he would just want any random variable, but I understand now. I'm sorry about all this confusion, I really appreciate you taking the time to help me understand it better.

So writing this would be; (A,B,C) = D

Would this work? I'm basically just writing the equation for a variable I don't know it's value in a sense? I'm more or less saying A, or, B or C = X?
No. There is no D. Where are you getting this D from?

In a truth table, each row represents the required output for one particular combination of input values.

For instance, in your problem the first row says that when A=0, B=0, and C=0 that the output should be zero, or X=0. The second row says that when A=0, B=0, and C=1 that the output should be 1, or X=1.

#### Joeaz123

Joined Nov 19, 2016
6
No. There is no D. Where are you getting this D from?

In a truth table, each row represents the required output for one particular combination of input values.

For instance, in your problem the first row says that when A=0, B=0, and C=0 that the output should be zero, or X=0. The second row says that when A=0, B=0, and C=1 that the output should be 1, or X=1.
I follow what you mean and get the inputs, but I still don't know how to answer what X is, is the answer (A,B,C) = X or X(A,B,C) = or am I just sending you around in circles now? If I am just say, I can ask my professor and sit down with him if I still haven't got it

#### WBahn

Joined Mar 31, 2012
25,765
Step back to how functions were expression in plain old algebra.

We might have say

y = f(x)

meaning that the value of the variable y is a function of the variable x. If you tell me what the value of x is, then I can tell you the value of y.

So three equivalent equations would be

y = 3x + 5

y(x) = 3x + 5

f(x) = 3x + 5

The only difference between y and y(x) is that we are explicitly showing what the independent variable is in the latter while we are requiring the reader to look over the equation in the former.

The same applies here. We have a variable X whose value depends on three variable, A, B, and C. So we can say

X = .... (some Boolean equation that contains A, B, and C)

or

X(A, B, C) = .... (some Boolean equation that contains A, B, and C)

Now look at your truth table. There are three rows that specify combinations of A, B, and C for which the value of X is supposed to be 1. So

X = 1 when the first such row applies OR the second such row applies OR the third such row applies.

The first such row applies when A=0 AND B=0 AND C=1.

Don't make it harder than it is!