I am new to Java Programming and have no clue what I'm doing. I have an assignment that involves base converting. I really need help getting started because I don't even understand the instructions. Here is the assignment:.
The simple math behind decimal-binary conversion algorithms
One algorithm for converting a base 10 number to another base b involves repeatedly dividing by b. Each time a division is. At each step, the dividend is the quotient from the preceding step; the. The algorithm stops when the quotient is 0. The number in the new base is the sequence of remainders in.
In this exercise you will use this algorithm to write a program that converts a base 10 number to a 4-digit number in another. The base 10 number and the new base. The start of the program is in the file BaseConvert.
The simple math behind decimal-binary conversion algorithms
Save this file to your. The program will only work correctly for base 10 numbers that fit in 4 digits in the new base. We know that in base 2 the. In base 8, the maximum. In general, the maximum base 10 number that fits in 4 base b.
Add an assignment statement to the program to compute this value for the base that is input and assign it. Add a statement that prints out the result appropriately labeled. Compile and run the. Now add the code to do the conversion. The comments below guide you through the calculations—replace them with the. So far the program does not print out the answer. Recall that the answer is the sequence of remainders written in reverse.
Since they are each integers, if we. So, we will use a variable of type String.This site offers several examples where representing a number in a base different from the customary 10 may have a great advantage.
For example, binary representation is instrumental in solving NimScoringTurning Turtles and other puzzles. As every one knows nowadays, this is also the system underlying the modern computer technology. Along with the binary, the science of computers employs bases 8 and 16 for it's very easy to convert between the three while using bases 8 and 16 shortens considerably number representations.
To represent 8 first digits in the binary system we need 3 bits. In order to obtain its binary representation, replace each of the four digits with the corresponding triple of bits: For the hexadecimal system conversion is quite similar, except that now one should use 4-bit representation of numbers below Thus it appears that the shortest way to convert numbers into the binary system is to first convert them into either octal or hexadecimal representation.
Now let see how to implement the general algorithm programmatically. For the sake of reference, representation of a number in a system with base radix N may only consist of digits that are less than N. Let's represent the algorithm mnemonically: result is a string or character variable where I shall accumulate the digits of the result one at a time.
I would like to have a function say called Conversion that takes two arguments M and N and returns representation of the number M in base N. The function might look like this.
As you see, at some point the function calls itself with a different first argument. One may say that the function is defined in terms of itself.Jave walk through: Number Base Conversion
Such functions are called recursive. The best known recursive function is factorial : n! The function calls applies itself to its arguments, and then naturally applies itself to its new arguments, and then We can be sure that the process will eventually stop because the sequence of arguments the first ones is decreasing. Thus sooner or later the first argument will be less than the second and the process will start emerging from the recursion, still a step at a time.
Not all programming languages Basic is one example allow functions to call themselves recursively. Recursive functions may also be undesirable if process interruption might be expected for whatever reason. For example, in the Tower of Hanoi puzzle, the user may want to interrupt the demonstration being eager to test his or her understanding of the solution. There are complications due to the manner in which computers execute programs when one wishes to jump out of several levels of recursive calls.
Note however that the string produced by the conversion algorithm is obtained in the wrong order : all digits are computed first and then written into the string the last digit first. Recursive implementation easily got around this difficulty. With each invocation of the Conversion function, computer creates a new environment in which passed values of M, N, and the newly computed S are stored.
Completing the function call, i. Recursive functions store a sequence of computations implicitly. Eliminating recursive calls implies that we must manage to store the computed digits explicitly and then retrieve them in the reversed order. It's best implemented with a stack data structure. Stack admits only two operations: push and pop.
Intuitively stack can be visualized as indeed a stack of objects. Objects are stacked on top of each other so that to retrieve an object one has to remove all the objects above the needed one. Obviously the only object available for immediate removal is the top one, i.
The function is by far longer than its recursive counterpart; but, as I said, sometimes it's the one you want to use, and sometimes it's the only one you may actually use. Contact Front page Contents Algebra. What is what?If you search the web for "How to convert from decimal to binary" you will find four simple algorithms: two for the integer and two for fractions. They are presented with examples below in the first part of the article.
In the second part this article explains the very basic math behind each of them. Knowing it may help you remember any of the algorithms if you suddenly forget them.
I strongly suggest you take a notepad and a pen and perform the operations along with me to better remember the math.
Here are the four algorithms with examples that you can find on the web. To convert integer to binary, start with the integer in question and divide it by 2 keeping notice of the quotient and the remainder.
Continue dividing the quotient by 2 until you get a quotient of zero. Then just write out the remainders in the reverse order. Here is an example of such conversion using the integer Now, we simply need to write out the remainder in the reverse order — So, 12 in decimal system is represented as in binary.
To convert fraction to binary, start with the fraction in question and multiply it by 2 keeping notice of the resulting integer and fractional part. Continue multiplying by 2 until you get a resulting fractional part equal to zero. Then just write out the integer parts from the results of each multiplication. Here is an example of such conversion using the fraction 0.
So, 0. To convert binary integer to decimal, start from the left. Take your current total, multiply it by two and add the current digit. Continue until there are no more digits left. Here is an example of such conversion using the fraction To convert binary fraction to decimal, start from the right with the total of 0.To get back the original number we count all the integers in the binary number we have 5.
We write from right to left the first 5 powers of two, starting with the power zero:. Now we multiply each of these numbers with their respective from the original binary number: Then we add each pair. We get:. Java code for converting from decimal to hex.
Clicking on a short link user will be automatically redirected to the original URL. There are many URL shortening services available online, like tiny. Implementing a URL shortening service is not a complex task, and it is often part of system design interviews. In this post, I will try to explain the process of implementing the service. Before implementation, it is always a good idea to write down what it is needed to be done in the form of functional and non-functional requirements.
Users need to be able to enter a long URL. Our service should save that URL and generate a short link. Users should have the option to enter the expiration date. After that date passed, the short link should be invalid. Let's say that we want to have a short link with a maximum length of 7. The most important thing in a URL shortener is the conversion algorithm. URL conversion can be implemented in several different ways, and each way has its pros and cons.
When using a hash function, it is sure that different inputs will result in different outputs. The result of the hash is longer than seven characters, so we would need to take the first seven characters. But, in this case, there could be a collision because the first seven characters could already be in use as a short link. Then, we take the next seven characters, until we find a short link that is not used.
The second way of generating a short link is by using UUIDs. The probability that a UUID will be duplicated is not zero, but it is close enough to zero to be negligible.
Since a UUID has 36 characters, that means that we have the same problem as above. We should take the first seven characters and check if that combination is already in use. The third way would be converting numbers from base 10 to base A base is a number of digits or characters that can be used to represent a particular number. Base 10 are digits , which we use in everyday life and base 62 are [a-z][A-Z]. This means that, for example, a number in base 10 with four digits would be the same number in base 62 but with two characters.
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Java Programming - Base Conversion...PLEASE HELP!?
I've been looking into the math behind converting from any base to any base. This is more about confirming my results than anything. I found what seems to be my answer on mathforum. I have the converting from a larger base to a smaller base down okay because it is simply take first digit multiply by base you want add next digit repeat. My problem comes when converting from a smaller base to a larger base. When doing this they talk about how you need to convert the larger base you want into the smaller base you have.
An example would be going from base 4 to base 6 you need to convert the number 6 into base 4 getting You then just do the same thing as you did when you were converting from large to small.
The difficulty I have with this is it seems you need to know what one number is in the other base. So I would of needed to know what 6 is in base 4. This creates a big problem in my mind because then I would need a table. Does anyone know a way of doing this in a better fashion. I thought a base conversion would help but I can't find any that work.
Shortening Strings (URLs) using Base 62 Encoding
And from the site I found it seems to allow you to convert from base to base without going through base 10 but you first need to know how to convert the first number from base to base. That makes it kinda pointless. Commenters are saying I need to be able to convert a letter into a number.
If so I already know that. That isn't my problem however. My problem is in order to convert a big base to a small base I need to first convert the base number I have into the base number I want.
In doing this I defeat the purpose because if I have the ability to convert these bases to other bases I've already solved my problem. Edit: I have figured out how to convert from bases less than or equal to 10 into other bases less than or equal to I can also go from a base greater than 10 to any base that is 10 or less. The problem starts when converting from a base greater than 10 to another base greater than Or going from a base smaller than 10 to a base greater than I don't need code I just need the basic math behind it that can be applied to code.
This seems a very basic question to me, so excuse me if I lecture you a bit. The most important point for you to learn here is that a number is not its digit representation.We want to convert a decimal number to binary with the arithmetic calculations done in binary. We can use nested multiplication as in Horner's Algorithm to represent a number:. As binary arithmetic is very tedious for us we would prefer to utilize the division algorithm and perform repeated division by the base recording the remainder each time.
Divide both sides of this equation by bthe remainder is then a 0repeat and the remainder is a 1then a 2etc. Converting a fraction to base b is as simple, just use repeated multiplication and recover the integer part each time until the desired accuracy is achieved.
Now the computer saves a lot of calculation time by using a table lookup. We can do the same thing in our math. Most of us have the binary numbers through 8 memorized. Converting from base 8 to base 2 is just a 3 digit lookup converting from hexadecimal to binary is just a 4 digit lookup.
Example Covert We will treat the integer and fraction parts separately for now. Complements in Radix r. Euclid's Division Algorithm.