Need help with discrete math

[P1X3]

 

How many decimal digits (with no leading 0s) are needed to represent the largest positive value that can be stored in a 54-bit two's complement binary format?

 

I have hard time understanding what this question is asking for. Could someone explain it?

 

We are talking about 54 bit signed value, so it's range must be -2^(n-1)~2^(n-1)-1 which in this case would be -2^53~(2^53)-1 -> -9007199254740992~9007199254740991

So in this case, would the answer be 16?

 

Edit: forgot negative sign. Also because question is talking about "positive" value, then is it ok to assume that we are talking about signed data?

Edited January 23, 2014 by P1X3

[Flojer0]

Looks right to me. And yes this is talking about signed data since that is what twos compliment is.

 

By "How many decimal digits (with no leading 0s) "  they mean base 10, or how we were all most likely taught how to count as kids, and by leading zeroes they mean any zeroes to the left of the number. So 000032 would not be considered any larger than 32 in the context of this question.

 

Aside from that you seem to understand the question fine. Is there anything I missed?

[P1X3]

I wasn't sure if the question was asking what I thought it was asking for. Thanks for clearing that up.

Noticed you are form Oregon too. Are you by any chance taking CS250 at PCC this term?

[Flojer0]

I wasn't sure if the question was asking what I thought it was asking for. Thanks for clearing that up.

Noticed you are form Oregon too. Are you by any chance taking CS250 at PCC this term?

Nope, I live down in Albany. Unfortunately life is getting busy enough school may not happen any time soon for me. But I'm attempting to make other provisions to further my career.

[P1X3]

Nope, I live down in Albany. Unfortunately life is getting busy enough school may not happen any time soon for me. But I'm attempting to make other provisions to further my career.

 

If I could get some help with 11 as well, that would be great. 9 and 10 I think I got them right, except the if-then part in 10

[Flojer0]

 

If I could get some help with 11 as well, that would be great. 9 and 10 I think I got them right, except the if-then part in 10

Well what exactly do you not understand? My discrete math isn't the most amazing thing so I can't give much of a walk through for each problem.

 

If it's an understanding the notation problem I found this Wikipedia page priceless when I was in school:

 

http://en.wikipedia.org/wiki/List_of_mathematical_symbols

[P1X3]

Well what exactly do you not understand? My discrete math isn't the most amazing thing so I can't give much of a walk through for each problem.

 

If it's an understanding the notation problem I found this Wikipedia page priceless when I was in school:

 

http://en.wikipedia.org/wiki/List_of_mathematical_symbols

 

I don't even know what to ask. I can kinda guesstimate the answer, but am unsure about it.

My instructor is teaching this course for first time, so she can help so much.

Getting in touch with actual discrete math instructor is almost impossible.

 

This class is just so different. Algebra was easy, Trig was easy, calculus is fun, but discrete math seems to require full concentration starting with logical predicates.

[Flojer0]

This class is just so different. Algebra was easy, Trig was easy, calculus is fun, but discrete math seems to require full concentration starting with logical predicates.

The problem I had was that we spend our whole lives having beaten into out heads that math is a routine  mechanical process. Then discrete math comes along and tells you your life is a lie and now you have to learn how to join your creative parts with your mathy parts. Possibly one of the most difficult things I've had to do mentally.

 

For the problems requiring you to write a negation I would recommend writing a truth table if you know how to do so. If I recall right they should be exact opposites, i.e. one in one where there are zeros in the other and visa versa.

 

For that last one. It looks to me like it is saying 'all values of x are in the set D, and P(x) is false. z is in the set D therefore ...' based on checking the symbols on the wikipedia page. If it helps I believe x is a universal qualifier here and z is a specific value. I think I know what conclusion I could draw but I'll let you see if I've given you any helpful ideas .

 

edit: Feel free to to use all the grains of salt necessary. As said I'm not well practiced in my discrete math.

[TideRower]

Your solution in 10 isn't right.

Just think what you'd do to proof that the statement is wrong: 

You'd search x,y in R such that ...

Hint: The "if clause" disappears in the negation. 

 

I thinkt in 11 you just need to write a consequence for "z in D"

[P1X3]

Your solution in 10 isn't right.

Just think what you'd do to proof that the statement is wrong: 

You'd search x,y in R such that ...

Hint: The "if clause" disappears in the negation. 

 

I thinkt in 11 you just need to write a consequence for "z in D"

 

Totally forgot about the if clause, but I think I got it now.

 

Also I made a mistake copying down 11 because it should be z not in D.

Statements:

• for all x in D, P(x) is false
• z is not in D

Therefore P(z) is true. I think... Yes? No?

 

Number 12 probably dosn't have conclusion because truth table for statements yields no critical rows where all statements are true. Is my reasoning right here?

 

[MikeD]

On 11:

The only thing you know is that anything belonging to D has the property that it makes P false. You can't say anything for things that are not in D (some may make P true, others false)

 

On 12:

You have P(x) is false as a premise, you can't have P(x) is true as a conclusion.

[TideRower]

Yes, now you got 10 right.

I don't really know about 11 and 12. I think you can't find a conclusion that makes the argument valid.

[arkon]

MikeD is right for #11. You know that for all x in D, P(x) is false, and z not in D, but anything outside of D could be true or false, since nothing is known about not D.

 

Not sure what #12 is asking, but if P is false, Q is trivially true.

[MikeD]

Not sure what #12 is asking, but if P is false, Q is trivially true.

 

Careful with that. If P(x) is false P(x) => Q(x) is true. But that does not mean Q(x) is true.

P => Q

P(x) is false

Then Q(x) is true

Is not a valid argument.

[P1X3]

Well, here is a method of proof chapter. I have no idea what I am doing.

Book makes no sense. I have some ideas down, but not a single clue how to prove or show them using any method of proof.

Edit: Since this is a nogo for me, I'll be dropping class, and changing majors...

answers.pdf

[BrightCandle]

You can however say that if P(z) is true then its not in D. 

[Ciccioo]

Edit: Since this is a nogo for me, I'll be dropping class, and changing majors...

that's sad to read, good luck with whatever you will try next

[BrightCandle]

Edit: Since this is a nogo for me, I'll be dropping class, and changing majors...

 

I have done and passed discrete maths at one of the top universities in the UK and my wife has a Maths degree from the top university in the UK and we think the question is extremely badly worded and we can't work out what the answer that your professor is digging for at all. P(z) is false is overall a true statement, but is that what he meant? Is it that simple or does P(y) have to be true and hence we are trying to prove why P(z) can't possible be true because since z is in forAll x in D, P(x) is false well then it follows logically that P(z) can't possible be true and you can do that by counter example. Its certainly not a good reason to drop the major, its a good reason however to go and see your professor and ask him what the hell the question means.