[Tutor] Modulus Operator ? SOLVED

[Ken Hammer]

Thanks, Danny

Got it.

Ken



In <CAGZAPF7O5LTq7q2DUpuoB7HqmpdcKd5Ks=_J9gDEr1_vOYo22Q at mail.gmail.com>, on 11/20/15 
   at 01:39 PM, Danny Yoo <dyoo at hashcollision.org> said:



>>>On Thu, Nov 19, 2015 at 1:11 PM, Ken Hammer <kfh777 at earthlink.net> wrote:
>>
>>>> y = 49%13
>>>> print y
>>>> 10
>>
>>>Actually, let me pretend for a moment that I don't know what the modulus
>>>operator is.  Why do we get 10 here?  Can you verbalize the reason?
>>
>> 49 contains 13 3 times and leaves 10 to be divided.
>>
>>
>>>Can you modify this example above to use the modulus operator with "10" on
>>>the right hand side?  What do you expect it computes?  What do you see?
>>
>> I see these.  Is this what you mean?  In view of the third float entry I don't understand why the first two are showing me the digits of the dividend.  Why doesn't y = 49%10 deliver 4 as an answer and with 100 as the divisor why don't I get 0?
>>
>>>>> y = 49%10
>>>>> print y
>> 9
>>>>> y= 49%100
>>>>> print y
>> 49
>>>>> 49/13.0
>> 3.7692307692307692



>Ok, I think I might see where're you getting stuck.

>You're misinterpreting what you read about the modulus operator. Contrary
>to what you've read, you don't use it a single time to get *all* the digits
>of the dividend all at once.  Rather, what it does do is let you probe at
>the *very last* digit in the number.  In that sense, when we're doing:

>    49 % 10

>What you're asking is what's left to be when we divide 49 by 10.

>    49 contains 10 4 times and leaves 9 to be divided.

>and that's why 49 % 10 == 9: it gives us the last, rightmost digit of the
>number.


>So you might be feeling a little let down.  What was it trying to say?
> I think the text was trying to say, when it talks about getting all the
>digits of a number, is that you can do *repeated* uses of division and
>modulus can get the individual digits.


>In a sense, division and modulus are like measuring tools that allow us to
>shift and probe at an object to figure out what it's made of. To make this
>concrete, imagine holding something underneath a microscope.  For our
>purposes, let's do this:

>############
>thing = 123456
>############


>But close your eyes for a moment: pretend for a minute that you don't know
>what this "thing" looks like.  What can we do to inspect it, if we don't
>want to look at it all at once?


>We can probe and shift it, to inspect portions of it.

>#############################
>def probe(x):
>     """Return the last digit of x."""
>     return x % 10

>def shift(x):
>    """Move x a little to the right, dropping the last digit."""
>    return x / 10
>#############################

>Here, we'll have two functions that we'll use on our thing.  But why do we
>call these things "probe" and "shift"?


>Because we can do things like this.  We can get the last digit...

>########################
>>>> probe(thing)
>6
>########################

>And now we know that this thing ends with a 6.  And we can move the thing
>around and probe again, to get the second to last digit...

>########################
>>>> probe(shift(thing))
>5
>########################

>So now we know this thing looks something like "...56"


>And we can repeat.  Shift the thing twice, and probe it to get the third to
>the last digit...

>########################
>>>> probe(shift(shift(thing)))
>4
>########################


>... and so on.


>Why is this useful?  In general: there are times when we're dealing with
>things that are REALLY large, things that we truly can't look at all at
>once, and knowing how to deal with just things by progressively poking and
>moving through it is a skill we can use to navigate through our data. 
>You'll hear the term "iteration", which is essentially what this is. 
>Exploring a number, using division and modulo operators, just happens to be
>a really simple toy example of this in action.

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K.F.Hammer Associates                                         Ken Hammer
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