# Number systems and binary codes

• ranju
In summary, the base is unknown and the short method involves adding the same number with a carry until you get a number that is three.
ranju

## Homework Statement

Given (135)x + (144)x = (323)x. What is the value of base x?
Now we can find out the value of x by simply converting to decimal both the sides , form a quadratic equation and solve but once in a random lecture our prof. taught us a kind of short method to solve this in less time followed by " here with base is unknown 5+4 is giving 3 , now 5+4 is 9 so we'll write digits from 0-8 and then further repeat it by adding the same with carry until we get 3.. See I am not sure that what I stated is correct.. I maybe skipping somet data.. So , I just wanted to know about this short method
what actually this method is like?? [/B]

## The Attempt at a Solution

In one method we simply convert in quadratic as : (1*x2 +3*x+5*x0) + (1*x2+4*x+4*x0) = 3*x2+2*x+3*x0
and x will come out to be 3[/B]

ranju said:

## Homework Statement

Given (135)x + (144)x = (323)x. What is the value of base x?
Now we can find out the value of x by simply converting to decimal both the sides , form a quadratic equation and solve but once in a random lecture our prof. taught us a kind of short method to solve this in less time followed by " here with base is unknown 5+4 is giving 3 , now 5+4 is 9 so we'll write digits from 0-8 and then further repeat it by adding the same with carry until we get 3.. See I am not sure that what I stated is correct.. I maybe skipping somet data.. So , I just wanted to know about this short method
what actually this method is like?? [/B]
First thing you should consider that the base cannot be smaller then "inside"numbers.Example ##(1204)_x## here x must be higher then 4, ##x>4##.You cannot write ##(143)_3##
Here the rule If you add 5+4 you get 9 but 9 is here 3 so.You need to think this way.First consider the rule which I wrote above Second there's a number ( which here x) , If I do this (9/x) remaining will be 3.

ranju said:
In one method we simply convert in quadratic as : (1*x2 +3*x+5*x0) + (1*x2+4*x+4*x0) = 3*x2+2*x+3*x0
and x will come out to be 3
Here x will not come out 3.The way of thinking is true.I mean equation is true but result is false

RyanH42 said:
If I do this (9/x) remaining will be 3.
I didn't get this , what is ths logic??

Given (135)x + (144)x = (323)x. What is the value of base x?
When the least significant digit of each is summed we know the result is nine and if we were working to base ten
we would write the resut as digit 9. But we are working in a base where this result is written as a 3.

So what do you conclude is the base?

NascentOxygen said:
what do you conclude is the base
but how to conclude about the base in this method??

NascentOxygen
ranju said:
but how to conclude about the base in this method??
Do you understand how positional notation and radix number systems work? If you don't have a solid grasp on that, you should study it before attempting this technique.

ranju said:
but how to conclude about the base in this method??
When you can't see a clear path, be adventurous: try various possibilities in turn and something will eventually leap out at you.

In the case in point, try ALL possible bases, one at a time.

phinds said:
Do you understand how positional notation and radix number systems work?
Yes I am quite familiar with it.. and I have solved it accordingly but about the short method I am confused..

ranju said:
Yes I am quite familiar with it...
Your statement in post #6 suggests that this is not true.

phinds said:
Your statement in post #6 suggests that this is not true
see about that radix number system , I have done with the conventional method as I stated in my question..but in the short method the picture is different ..if 5+5 =4 and we are getting 3 for base x in the result , how to take the possibilities that's the problem..!

NascentOxygen said:
In the case in point, try ALL possible bases, one at a time.
How to try the possibilities ..?? what I am seeing your answer is to compare both sides ..is it so??

ranju said:
see about that radix number system , I have done with the conventional method as I stated in my question..but in the short method the picture is different ..if 5+5 =4 and we are getting 3 for base x in the result , how to take the possibilities that's the problem..!
Here's a three digit number: 1 3 5
I haven't told you the base it is written in. ( I'll give you a hint: it is not binary!)
What possible bases might it have? List some of them.

ranju said:
...if 5+5 =4 and we are getting 3 for base x in the result ...
Huh? Where did that set of numbers come from?

NascentOxygen said:
What possible bases might it have?
the base will be any number greater than 5..!

phinds said:
Huh? Where did that set of numbers come from?
sorry its 5+4 .. these are the LSBs of the given problem..!

ranju said:
the base will be any number greater than 5..!
Right!

So work your way up through the first dozen of these possibilities, applying it to the arithmetic expression in your first post.

ranju said:
sorry its 5+4 .. these are the LSBs of the given problem..!
Right. So now we're back to NascentOxygen's question in post #5, which you never answered, which led me to believe that you don't have a good understanding of positional notation and radix number systems. If you did have that understanding, you would not have even asked the question, so I again suggest that you go back to the basics and learn them before trying to apply them.

Look, I'm not trying to insult you or give you a hard time. We see this all the time here on the forum. Someone feels that they have a good grasp of particular material but their questions make it clear that this is not the case. In such cases, I always feel that it's a good idea for them to go back to the basics.

If you don't want to do that then NascentOxygen has given you enough hints to lead you to the answer for this particular problem and ones similar to it (but possibly not enough to generalize to all such radix number system problems, which is why I suggest going back to the basics).

Last edited:
NascentOxygen said:
Right!

So work your way up through the first dozen of these possibilities, using the arithmetic expression in your first post.
that's the problem actually I tried this thing..if we see as a whole all and all base 6 suits it..b
phinds said:
Right. So now we're back to NascentOxygen's question in post #5, which you never answered, which led me to believe that you don't have a good understanding of positional notation and radix number systems. If you did have that understanding, you would not have even asked the question, so I again suggest that you go back to the basics and learn them before trying to apply them.

Look, I'm not trying to insult you or give you a hard time. We see this all the time here on the forum. Someone feels that they have a good grasp of particular material but their questions make it clear that this is not the case. In such cases, I always feel that it's a good idea for them to go back to the basics.

If you don't want to do that then NascentOxygen has given you enough hints to lead you to the answer for this particular problem and ones similar to it (but possibly not enough to generalize to all such radix number system problems, which is why I suggest going back to the basics).
it will be better if you just have a look..I answered his question...
And by the way ..the doubt is clear by now to me...

So you are all sorted now? Make up some exercises for yourself as practice, so you don't forget again.

Try this quick one: ##\mathrm {\ \left(523\right)_x\ +\ \left(117\right)_x\ =\ (641)_x}##

Determine x.

Be ambitious, try some with a hexadecimal base.

NascentOxygen said:
So you are all sorted now? Make up some exercises for yourself as practice, so you don't forget again.

Try this quick one: ##\mathrm {\ \left(523\right)_x\ +\ \left(117\right)_x\ =\ (641)_x}##

Determine x.

Be ambitious, try some with a hexadecimal base.
it'll be 9...

NascentOxygen

## 1. What are number systems and why are they important in computer science?

Number systems are a way of representing and manipulating numbers. They are important in computer science because computers use binary code, a number system with only two digits (0 and 1), to process and store data. Understanding different number systems is crucial for understanding how computers work.

## 2. How is binary code used in computers?

Binary code is the foundation of all computer operations. It uses combinations of 0s and 1s to represent and process data. These 0s and 1s are interpreted as electrical signals by the computer's hardware, allowing it to perform calculations and execute commands.

## 3. What are the different types of number systems?

There are many different types of number systems, including decimal, binary, octal, hexadecimal, and more. Each system has its own unique way of representing and manipulating numbers.

## 4. How do you convert numbers from one number system to another?

Converting numbers from one number system to another involves understanding the place value and digit values of each system. For example, in binary code, each digit represents a power of 2, while in decimal, each digit represents a power of 10. Converting between systems involves breaking down the original number into its component parts and then reassembling it in the desired number system.

## 5. How are binary codes used in data storage?

Binary codes are used to store and represent data in a computer's memory. Each piece of data is translated into binary code, which can then be stored in the form of 0s and 1s. This allows for efficient and compact storage of large amounts of data, as well as quick retrieval and processing by the computer.

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