Basic Logic Gates / Pulse Train Problem (Includes Solution)

[s3a]

Homework Statement

The problem and its solution are attached.

Homework Equations

N/A

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!

 

[mfb]

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]

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]

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]

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]

So, A is a sequence of digits

A pulse train, right (where the individual bits are "wagons").

 

[s3a]

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]

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]

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. :)