The Hexadecimal number system as the name suggests comprises 16 entities. These 16 entities consist of 10 digits, 0-9 representing the first 10 numbers of the hexadecimal system as well. For the remaining 6 numbers, we use English alphabets ranging from A through F to represent the numbers 10 to 15. It should be noted that the lowest number in the hexadecimal system is 0 with the highest being 15 represented by F. A hexadecimal number can be derived from a binary number by clubbing 4 digits to constitute a single character of the hexadecimal number.
Example:
Input: 11011111 Output: DF Input: 10001101 Output: 8D
- In the above example, the binary number 10001101 can be broken down into chunks of 4 bits such as 1000 and 1101 which act as 2 characters for the corresponding hexadecimal number.
- The resultant hexadecimal number would be 8D where every character is determined by calculating its corresponding value in the decimal system and replacing it with an alphabet if it is a two-digit number in this case D which represents 13. The hexadecimal system is also referred to as base-16.
For the conversion of binary to hexadecimal, we are going to use the following two approaches :
- Using the toHexString() builtin java method
- Repeatedly getting the remainder and dividing the converted decimal number by 16
Approach 1:
Using this approach, we first convert the binary number to a decimal number which is stored as an Integer. Then, we simply use the toHexString() method of java to generate the desired output string.
Syntax :
public static String toHexString(int num)
Parameter:
- num – This parameter specifies the number which is to be convertedÂ
to a Hexadecimal string. The data-type is int.
Return Value: The function returns a string representation of the int argument as an unsigned integer in base 16.
Algorithm :
- Convert the binary number to a decimal number.
- To convert the binary number to a decimal number, first, extract each digit using by getting the remainder by dividing by 10.
- Next, multiply this digit with increasing powers of 2.
- Keep on dividing the original binary number by 10 to eliminate the last digit in each iteration.
- After having gotten the decimal number, just use the toHexString() method to get the desired output.
Example:
Java
// Java program to convert binary to hexadecimalÂ
class GFG {Â
    // method to convert binary to decimal    int binaryToDecimal(long binary)    {Â
        // variable to store the converted        // binary number        int decimalNumber = 0, i = 0;Â
        // loop to extract the digits of the binary        while (binary > 0) {Â
            // extracting the digits by getting            // remainder on dividing by 10 and            // multiplying by increasing integral            // powers of 2            decimalNumber                += Math.pow(2, i++) * (binary % 10);Â
            // updating the binary by eliminating            // the last digit on division by 10            binary /= 10;        }Â
        // returning the decimal number        return decimalNumber;    }Â
    // method to convert decimal to hexadecimal    String decimalToHex(long binary)    {        // variable to store the output of the        // binaryToDecimal() method        int decimalNumber = binaryToDecimal(binary);Â
        // converting the integer to the desired        // hex string using toHexString() method        String hexNumber            = Integer.toHexString(decimalNumber);Â
        // converting the string to uppercase        // for uniformity        hexNumber = hexNumber.toUpperCase();Â
        // returning the final hex string        return hexNumber;    }Â
    // Driver Code    public static void main(String[] args)    {Â
        // instantiating the class        GFG ob = new GFG();Â
        long num = 10011110;               // calling and printing the output        // of decimalToHex() method        System.out.println("Inputted number : " +num);        System.out.println(ob.decimalToHex(10011110));    }} |
Output
Inputted number : 10011110 9E
Time complexity: O(log N) where N is the input binary number, since the number of iterations in the while loop is proportional to the number of digits in the binary number.
Auxiliary space: O(1)
Approach 2:Â
- Under the second approach, we again first convert the binary number to a decimal number.
- Then we continuously divide and get the remainder of this decimal number to get the single character for each set of 4 bits we can find in the original binary number.
Algorithm:Â
- Convert the binary to a decimal using steps 2-4 in the above algorithm.
- Next, run a while loop with the terminating condition that the decimal number becomes 0 and the updating condition that the decimal number is divided by 16 in each iteration.
- In each iteration get the remainder by dividing the number by 16.
- Constitute a new String and keep on adding characters which are the remaining on dividing by 16.
- If the remainder is greater than or equal to 10 replace it with alphabets A-F depending on the remainder.
Example:Â
Java
// Java program to convert binary to hexadecimalÂ
class GFG {Â
    // method to convert binary to decimal    int binaryToDecimal(long binary)    {Â
        // variable to store the converted binary        int decimalNumber = 0, i = 0;Â
        // loop to extract digits of the binary        while (binary > 0) {Â
            // extracting each digit of the binary            // by getting the remainder of division            // by 10 and multiplying it by            // increasing integral powers of 2            decimalNumber                += Math.pow(2, i++) * (binary % 10);Â
            // update condition of dividing the            // binary by 10            binary /= 10;        }Â
        // returning the decimal        return decimalNumber;    }Â
    // method to convert decimal to hex    String decimalToHex(long binary)    {Â
        // variable to store the output of        // binaryToDecimal() method        int decimalNumber = binaryToDecimal(binary);Â
        // character array to represent double        // digit remainders        char arr[] = { 'A', 'B', 'C', 'D', 'E', 'F' };Â
        // variable to store the remainder on        // division by 16        int remainder, i = 0;Â
        // declaring the string that stores the        // final hex string        String hexNumber = "";Â
        // loop to convert decimal to hex        while (decimalNumber != 0) {Â
            // calculating the remainder of decimal            // by dividing by 16            remainder = decimalNumber % 16;Â
            // checking if the remainder is >= 10            if (remainder >= 10)                               // replacing with the corresponding                // alphabet from the array                hexNumber = arr[remainder - 10] + hexNumber;                       else                               hexNumber = remainder + hexNumber;Â
            // update condition of dividing the            // number by 16            decimalNumber /= 16;        }Â
        // returning the hex string        return hexNumber;    }Â
    // Driver Code    public static void main(String[] args)    {Â
        // instantiating the class        GFG ob = new GFG();Â
        long num =11000011;               // printing and calling the        // decimalToHex() method        System.out.println("Input : "+num);        System.out.println("Output : " +ob.decimalToHex(num));    }} |
Output
Input : 11000011 Output : C3
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