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Basic Logic Gates / Pulse Train Problem (Includes Solution)

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s3a
#1
Feb9-13, 01:44 PM
P: 554
1. The problem statement, all variables and given/known data
The problem and its solution are attached.

2. Relevant equations
N/A

3. The attempt at a solution
I'm very confused about how output pulse trains work. I already checked online (including Wikipedia) so, could someone please give me an explanation of the absolute basics in an easy-to-understand way?

I'm confused about what the “rectangle-ness” around the numbers is for and how it works.

What I DO get is that the output is the same as the input A since input B is a constant 1 and, converting “1” to “True”, we get unknown AND True = unknown.

Any input for helping me fully understand this problem would be greatly appreciated!
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TheProblemAndSolution.jpg  
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mfb
#2
Feb9-13, 02:13 PM
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P: 11,573
I'm confused about what the “rectangle-ness” around the numbers is for and how it works.
That is just a graphical representation of the input - the line is high for 1 and low for 0.
s3a
#3
Feb9-13, 03:38 PM
P: 554
Oh but, how do I know what A (and, by consequence, Y) is equal to?

In other words, what is the computational step (no matter how simple it may be)?

mfb
#4
Feb9-13, 03:42 PM
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P: 11,573
Basic Logic Gates / Pulse Train Problem (Includes Solution)

That is given there. Input A starts with a 1 (written above "a"), this is followed by a 0 ("b"), ...
Well, it could start with "h" as well, but that changes nothing.
s3a
#5
Feb9-13, 03:50 PM
P: 554
So, A is a sequence of digits rather than one final answer?

I was thinking it would be (a OR b OR c OR d OR e OR f OR g OR h) = (0 or 1) = A or something like that. (By a capital "OR", I am referring to boolean logic whereas with the lowercase "or", I am just stating that the final value of A is either a 0 or a 1.)

I'm still confused. (Sorry.)
mfb
#6
Feb9-13, 03:51 PM
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P: 11,573
So, A is a sequence of digits
A pulse train, right (where the individual bits are "wagons").
s3a
#7
Feb9-13, 04:02 PM
P: 554
1) Is the "rectangle-ness" part of the value A or is it just a fancy graphical drawing to what A really is which is only the individual digits (=wagons, as you mentioned in your last post)?

2) Is Y = {(a AND B),(b AND B),(c AND B),(d AND B),(e AND B),(f AND B),(g AND B),(h AND B)} = {(1 AND 1),(0 AND 1),(0 AND 1),(1 AND 1),(1 AND 1),(0 AND 1),(1 AND 1),(0 AND 1)}

3) Is a pulse train a SET of values (in the mathematical sense)?
mfb
#8
Feb9-13, 04:06 PM
Mentor
P: 11,573
Quote Quote by s3a View Post
1) Is the "rectangle-ness" part of the value A or is it just a fancy graphical drawing to what A really is which is only the individual digits (=wagons, as you mentioned in your last post)?
It is the same as the written "0" and "1" - just another way to graph them.

2) Is Y = {(a AND B),(b AND B),(c AND B),(d AND B),(e AND B),(f AND B),(g AND B),(h AND B)} = {(1 AND 1),(0 AND 1),(0 AND 1),(1 AND 1),(1 AND 1),(0 AND 1),(1 AND 1),(0 AND 1)}
3) Is a pulse train a SET of values (in the mathematical sense)?
A sequence of values, they have some order.
s3a
#9
Feb9-13, 04:10 PM
P: 554
I think I get it now (thanks to what you said combined with looking at problems later in the book where B is not a constant 1 and applying what I now know).

Thanks. :)


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