Java Convert Decimal to Binary

Converting a decimal number to binary is a fundamental operation in computer science and programming. Binary is a base-2 numeral system, meaning it only uses two digits, 0 and 1. In contrast, the decimal system, which we use daily, is a base-10 numeral system that uses digits from 0 to 9.

Understanding Decimal and Binary Systems:

In the decimal system, each digit's position represents a power of 10. For instance, in the number 123, the '3' represents the unit, '2' represents tens, and '1' represents hundreds.

Similarly, in the binary system, each digit's position represents a power of 2. For example, in the binary number 101, the '1' represents the unit, '0' represents twos, and '1' represents fours.

Conversion Process

To convert a decimal number to binary, you repeatedly divide the decimal number by 2 and keep track of the remainders.

You start by dividing the decimal number by 2 and note down the remainder. Then, you continue dividing the quotient by 2, and so on, until the quotient becomes 0.

Finally, you write down the remainders in reverse order to obtain the binary representation.

1) Using StringBuilder and Modulo Division

This method involves repeatedly dividing the decimal number by 2 and keeping track of the remainders. The remainders are then used to construct the binary representation in reverse order.

Steps:

1. Initialize a StringBuilder: Create a StringBuilder object to store the binary representation.
2. Modulo Division Loop: Start a loop that continues until the decimal number becomes 0.
   • Calculate the remainder when dividing the decimal number by 2.
   • Prepend the remainder to the StringBuilder.
   • Update the decimal number by integer division (divide by 2) to get the next quotient.
3. Handling the Case of Zero Decimal: If the input decimal was initially 0, append "0" to the StringBuilder to represent the binary number "0".
4. Return Binary Representation: Convert the StringBuilder to a String and return it as the binary representation.

Let's implement the above steps in a Java program.

DecimalToBinary.java

Output:

 Binary representation of 10 is: 1010 

2) Using Bitwise Operators

This method leverages bitwise operators, specifically the right shift (>>) and bitwise AND (&) operators, to extract each bit of the decimal number's binary representation.

Steps:

1. Initialize a StringBuilder: Create a StringBuilder object to store the binary representation.
2. Bitwise Operation Loop: Start a loop that iterates 32 times, corresponding to the 32 bits in an integer.
   • Right shift the decimal number by the current iteration index (decimal >> i). This moves the bit at position i to the rightmost position.
   • Perform a bitwise AND operation with 1 (& 1). This extracts the least significant bit (LSB) of the shifted decimal number.
   • Append the extracted bit to the StringBuilder.
3. Trim Leading Zeros: Trim any leading zeros from the StringBuilder's binary representation.
4. Handling the Case of Zero Decimal: If the input decimal was initially 0, append "0" to the StringBuilder to represent the binary number "0".
5. Return Binary Representation: Convert the StringBuilder to a String and return it as the binary representation.

Let's implement the above steps in a Java program.

DecimalToBinary.java

Output:

 Binary representation of 10 is: 1010 

3) Using Integer.toBinaryString() Method

This method utilizes the Integer.toBinaryString() static method provided by Java's Integer class. This method converts an integer to its binary string representation.

Steps:

1. Call Integer.toBinaryString(): Pass the decimal number as an argument to the Integer.toBinaryString() method.
2. Return Binary Representation: The method returns the binary representation of the decimal number as a String.

The Integer.toBinaryString() method converts decimal to binary string. The signature of the toBinaryString() method is given below:

Let's implement the above steps in a Java program.

DecimalToBinary.java

Output:

 Binary representation of 10 is: 1010 

4) Using Math.pow() Function

This method calculates each bit of the binary representation of the decimal number using Math.pow(). It determines the number of bits required to represent the decimal number and then iterates through each bit position, calculating the bit value based on its position.

Steps:

1. Check for Zero Decimal: If the decimal number is 0, return "0" as its binary representation.
2. Calculate Number of Bits: Calculate the number of bits needed to represent the decimal number. This is done by taking the logarithm base 2 of the decimal number and adding 1. It gives us the minimum number of bits required to represent the decimal number.
3. Iterate Through Each Bit Position:
   • Start iterating from the most significant bit position (highest power of 2) to the least significant bit position (lowest power of 2).
   • Calculate the bit value for each position using Math.pow(2, i), where i is the current bit position.
4. Check Bit Value:
   • Perform a bitwise AND operation between the decimal number and the calculated bit value.
   • If the result is 0, the bit at that position is 0; otherwise, it's 1.
   • Append the corresponding character ('0' or '1') to the binary representation.
5. Construct Binary Representation: After iterating through all bit positions, the binary representation is constructed.
6. Return Binary Representation: Return the constructed binary representation as a String.

Let's implement the above steps in a Java program.

DecimalToBinary.java

Output:

 Binary representation of 10 is: 1010 

5) Using Recursive Approach

This method employs a recursive algorithm to convert a decimal number to its binary representation. It divides the decimal number by 2 recursively and constructs the binary representation digit by digit.

Steps:

Base Cases:

• If the decimal number is 0, return "0" as its binary representation.
• If the decimal number is 1, return "1" as its binary representation.

1. Recursive Call: For decimal numbers greater than 1, recursively call the decimalToBinary method with the quotient obtained by dividing the decimal number by 2.
2. Concatenate Remainder: After the recursive call, concatenate the remainder obtained by % 2 to the binary representation obtained from the recursive call.
3. Return Binary Representation: Return the constructed binary representation as a String.

Let's implement the above steps in a Java program.

DecimalToBinary.java

Output:

 Binary representation of 10 is: 1010 

6) Using a Stack

This method employs a stack data structure to store the binary digits of the decimal number in reverse order. It iterates through the decimal number, extracting each bit using bitwise AND operation, and pushes the bits onto the stack. After processing all bits, it pops them from the stack to construct the binary representation.

Steps:

1. Base Case: If the decimal number is 0, return "0" as its binary representation.
2. Iterate Through Decimal Number:
   • Iterate through the decimal number until it becomes 0.
   • Extract each bit of the decimal number using bitwise AND operation with 1 (decimal & 1).
   • Push the bit onto the stack.
3. Construct Binary Representation: After processing all bits, pop them from the stack to construct the binary representation.
4. Return Binary Representation: Return the constructed binary representation as a String.

Let's implement the above steps in a Java program.

DecimalToBinary.java

Output:

 Binary representation of 10 is: 1010 

7) Using Custom Logic

We can convert decimal to binary in Java using custom logic.

DecimalToBinaryExample.java

Output:

 Decimal of 10 is: 1010 Decimal of 21 is: 10101 Decimal of 31 is: 11111 

8) Using Arrays

DecimalToBinaryUsingArrays.java

Output:

 Binary representation of 10 is: 10100000000000000000000000000000