Convert From Any Base to Decimal and Vice Versa in Java

5 May 2025 | 5 min read

Calculate the decimal representation of a given number and its base. Any number that can be represented by the numbers 0 through 9 and A through Z can be used as the base of the number. The value of A is 10, and the value of B is 11, and so on. The number can be converted to decimal by implementing a function.

Example 1:

Input:

Output:

The equivalent value is 485

Explanation:

The formula that follows is used to convert the octal number 745 to decimal: (7 * 8^2) + (4 * 8^1) + (5 * 8^0) = 448 + 32 + 5 = 485

Example 2:

Input:

Output:

The equivalent value is 11

Explanation:

The following formula is used to convert the binary number 1011 to decimal: (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11.

Example 3:

Input:

Output:

The equivalent value is 675

Explanation:

The following formula is used to convert the Hexadecimal 2A3 to decimal: (2 × 16^2) + (A × 16^1) + (3 × 16^0) = 512 + 160 + 3 = 675, where 'A' represents the 0 in hexadecimal. Thus, 2A3 in hexadecimal is 675 in decimal.

Example 4:

Input:

Output:

The equivalent value is 10010.

Explanation:

To convert 18 to binary, keep track of the remainder after continuously dividing by 2:

18 ÷ 2 = 9 remainder 0

9 ÷ 2 = 4 remainder 1

4 ÷ 2 = 2 remainder 0

2 ÷ 2 = 1 remainder 0

1 ÷ 2 = 0 remainder 1

The binary is 10010 when read from the bottom to the top.

Example 5:

Input:

Output:

The equivalent value is FF.

Explanation:

The hexadecimal representation of 255 is FF, which may be obtained by repeatedly dividing by 16 and taking the remainders: 255 ÷ 16 = 15 (F) remainder 15 (F). Hence, the value is FF.

Approach: Naïve

A character can be converted to its equivalent integer value using the value function defined in the code, and base-to-decimal conversion can be done using the toDeci function. By changing their ASCII values, the value function works with both alphabetic characters and numeric digits. The toDeci function multiplies the value of each character by the matching power of the base as it iterates across the string from right to left. Invalid digits-those that exceed the base-are checked for, and if found, an error is returned.

Implementation:

FileName: baseTodecimal.java

Output:

 
The Decimal equivalent of the 2A3 with the base 16 is given as 675

Complexity Analysis:

The time complexity of the above code is O(N), where 'N' represents the length of the string, and the space complexity is O(1).

How to do the reverse?

Approach: Naïve

The code implements a decimal-to-any-base conversion scheme. With support for both numeric and alphanumeric digits up to base 36, the revValue method determines the character representation for an integer value. In order to create the proper base representation, the fromDecimal method calculates remainders, transforms them into characters, and then reverses the resultant sequence.

Implementation:

FileName: DecimalConversion.java

Output:

 
The Equivalent of the 282 with the base 16 is 11A

Complexity Analysis:

The Time Complexity is O(logbasen) where 'n' is the input number the 'base' represents the to which the number is to be converted and the space complexity is O(logbasen).

Approach: Using Integer.parseInt()

A string representation of a number in the given base (radix) is converted to its decimal integer equivalent using the Integer.parseInt(String s, int radix) method, as the code shows.