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# Converting a Number from One Base to Another in Java

Last modified: January 20, 2023

## 1. Overview

In this tutorial, we'll explore how to **convert a number from one base to another in Java**. There would be two approaches used in converting a number from, let's say, base 2 to base 5 and vice versa.

## 2. The *Integer* class

The *java.lang* package has the *Integer* class, a wrapper class, that wraps a primitive type *int* to an *Integer* object. This class has several methods for manipulating an *int* and for converting an int to a* String* object and a *String* to an *int* type. **The parseInt() and toString() methods would be needed to help us convert numbers from one base to another**.

### 2.1. *parseInt()* Method

The *parseInt()* method has two parameters: *String* s and *int* *radix:*

`public static int parseInt(String s, int radix)`

**It returns an integer value of the given string argument in the specified radix given as the second argument**. The string argument must be digits in the radix specified. It also throws a *NumberFormatException* in situations mentioned in Java's official documentation.

### 2.2. *toString()* Method

The *toString()*Â method is used in conjunction with the earlier mentioned *parseInt()* method to convert numbers from one base to another:

`public static String toString(int i, int radix)`

According to its signature, this method takes two parameters, *int* *i* and a *radix* of type *int.*Â **The method returns a string representing the value of the specified radix, which is the second argument**. Where a second argument is not provided, it uses base 10 as the default value.

## 3. Converting Number Bases Using *Integer* Class Methods *parseInt()*Â and *toString()*

As we hinted earlier, there are two approaches for converting a number from one base to another in Java. The first and easiest way would be using the *Integer* class methods *parseInt()* and *toString()* to make this number of conversions from a given base to a target base. Let's create a method that uses both *parseInt()* and *toString()* for base conversion:

```
public static String convertNumberToNewBase(String number, int base, int newBase){
return Integer.toString(Integer.parseInt(number, base), newBase);
}
```

Our method, *convertNumberToNewBase(),* takes three parameters, a string representing digits in a specified radix or a number base system of the second argument of type *int*. The third argument is an *int*Â of the new base for our conversion. The method returns a string in the new base. The *parseInt()* takes the string argument and its radix and returns an integer value. This integer value is passed on as the first argument of the *toString()* method, which converts the integer to a string in the new base given in its second argument.

Let's look at an example:

```
@Test
void whenConvertingBase10NumberToBase5_ThenResultShouldBeDigitsInBase5() {
assertEquals(convertNumberToNewBase("89", 10, 5), "324");
}
```

The string* “89”* is given in base 10 for conversion to base 5. Our method returns a string result *“324”,* which is indeed a number in the base 5 number system.

## 4. Converting Number Bases Using a Custom Method

Our other approach for converting between number bases would be writing our own custom method in Java for executing this task. The proposed method should have three parameters, a string of digits, an *int* specifying base, and another *int* representing the new base for conversion.

A logical way to achieve this is to create sub-methods to handle smaller aspects of our number conversion code. We'll define a method for converting any number from base 2 to 9 and 16 to decimal (base 10) and another for converting numbers from base 10 to base 2 to 9 and 16:

```
public static String convertFromDecimalToBaseX(int num, int newBase) throws IllegalArgumentException {
if ((newBase < 2 || newBase > 10) && newBase != 16) {
throw new IllegalArgumentException("New base must be from 2 - 10 or 16");
}
String result = "";
int remainder;
while (num > 0) {
remainder = num % newBase;
if (newBase == 16) {
if (remainder == 10) {
result += 'A';
} else if (remainder == 11) {
result += 'B';
} else if (remainder == 12) {
result += 'C';
} else if (remainder == 13) {
result += 'D';
} else if (remainder == 14) {
result += 'E';
} else if (remainder == 15) {
result += 'F';
} else {
result += remainder;
}
} else {
result += remainder;
}
num /= newBase;
}
return new StringBuffer(result).reverse().toString();
}
```

The *convertFromDecimalToBaseX()* method takes two parameters, an integer and a new base for conversion. **The result is obtained by continuously dividing the integer by the new base and taking the remainder**. The method also has a conditional for base 16 numbers.Â Another method converts from any given base to base 10 with a sub-method for converting base 16 char characters to decimal values:

```
public static int convertFromAnyBaseToDecimal(String num, int base) {
if (base < 2 || (base > 10 && base != 16)) {
return -1;
}
int val = 0;
int power = 1;
for (int i = num.length() - 1; i >= 0; i--) {
int digit = charToDecimal(num.charAt(i));
if (digit < 0 || digit >= base) {
return -1;
}
val += digit * power;
power = power * base;
}
return val;
}
public static int charToDecimal(char c) {
if (c >= '0' && c <= '9') {
return (int) c - '0';
} else {
return (int) c - 'A' + 10;
}
}
```

We combine these methods to have a robust method that converts numbers from any base to another:

```
public static String convertNumberToNewBaseCustom(String num, int base, int newBase) {
int decimalNumber = convertFromAnyBaseToDecimal(num, base);
String targetBase = "";
try {
targetBase = convertFromDecimalToBaseX(decimalNumber, newBase);
} catch (IllegalArgumentException e) {
e.printStackTrace();
}
return targetBase;
}
```

Let's test our custom method to confirm it works as expected:

```
@Test
void whenConvertingBase2NumberToBase8_ThenResultShouldBeDigitsInBase8() {
assertEquals(convertNumberToNewBaseCustom("11001000", 2, 8), "310");
}
```

The method returns the string *“310”* when the string “11001000” in base 2 is converted to base 8.

## 5. Conclusion

In this tutorial, we learned how to convert numbers from one base to another in Java using the* java.lang.Integer* class methods *toString()* and *parseInt().* We put these two methods into another method for reusability. We also took it a step further by writing our own custom method, which converts a string of digits to its base 10 equivalent and then converts it to another number base.

The entire code for this tutorial can be foundÂ over on GitHub.