# Question about logic gates

Discussion in 'Homework Help' started by TL314, Apr 15, 2015.

1. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
What logic gate is the AB with a bar on top? Trying to figure out how to solve this. Thanks!

2. ### WBahn Moderator

Mar 31, 2012
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Do know what the bar indicates?

3. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
no im not sure

4. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
is it inverse?

5. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Then you probably need to go back and read through the basic intro material to digital logic again -- there's probably other things you've missed.

The overbar is one way of indicating logical inversion (or NOT).

$
\text{Y\;=\;\bar{A}\;=\;NOT(A)\;=\;A'}
$

If A is True, then Y is False, while if A is False then Y is True.

6. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
[
Yes.

So, with that in mind, what would

$
\text{Y \; = \; \bar{\bar{A}}}
$

be equal to?

7. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Also, note that X and Y below are NOT equal.

$
\text{X = \bar{A}\.\bar{B}}
\text{Y = \bar{A\.B}}
$

Because of this, and because it is easy for adjacent overbars to accidentally be joined, either by the person reading it or by the software rendering it, it is best to use parens to make it very clear what the groupings are.

$
\text{X = $$\bar{A}$$$$\bar{B}$$}
\text{Y = \bar{$$AB$$}}
$

8. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
is this the same as my (AB) bar question?
that would be A?
y does your have 2 solid bars while mine is 1 solid and 1 split?

9. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Yes, A double bar is just A.

The solid versus split is critical.

If you have AB with a solid overbar, it means that you AND the signals A and B together and THEN negate the result.

If you have AB with a split overbar, it means that you negate A and B separately and THEN you AND the results.

Last edited: Apr 15, 2015
10. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
so then would my (AB) with a solid and split just be AB?

11. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
NO! The difference is CRITICAL!

It is the difference between saying that the bomb will explode anytime that [(light A is on) AND (light B is on)] is False and saying that the bomb will explode anytime that [(light A is NOT on) AND (light B is NOT on)] is True. In the latter case, it's pretty clear that bomb will only explode if both lights are off, so that as long as one of the lights is on, the bomb blows up. But in the former case, both lights have to be on in order for the bomb to detonate.

The overbar is an implicit pair of parentheses -- everything under the bar is evaluated and then THAT result is negated.

Mar 29, 2015
64
0
confused

13. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
im going to try and attempt my hw problem, i know im just trying random things but I think this would work.
A AND gate gives me AB
A NAND gates gives me AB(bar)
A OR gates gives me (A+B)
so if I have those 3 hooked to a OR gate my output would be AB+AB(bar)+(A+B) right?

14. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Yes, but what is it you are trying to accomplish?

In your original post you said you were trying to solve an equation that had three Boolean terms? What does "solving" mean for this homework?

I had assumed that it probably meant simplifying that expression into something that had fewer terms.

15. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Draw a circuit that implements the X and the Y that were presented in Post #7.

Draw the truth table for both.

16. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
I have to create a circuit that satisfies that equation. So I need OR gates to sum and ill sum the 3 individual gates to give a single output C. So in my attempt I did a AND a NAND and a OR summed through a OR gate so I think it would give me that equation but i could be completely wrong

17. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
It will give you a solution, but you can achieve the same solution (i.e., the same function) with a single two-input logic gate.

18. ### TL314 Thread Starter Member

Mar 29, 2015
64
0
1 gate will give me that solution? how?

19. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
There are several ways to see how. Let's work through a couple of them.

The gold standard for digital logic is the truth table.

So draw the truth table for that function. Since it only has two inputs, there are only four rows. Once you do that, see if you recognize the logic function that is implemented.

20. ### DerStrom8 Well-Known Member

Feb 20, 2011
2,428
1,329
Don't forget that a NOT gate can be combined with an AND or an OR to get two new gates....

Sorry if that was too much of a hint WBahn. Your'e doing well, I should probably leave you to it.