The Hexadecimal is a very useful Number System based on the premise of clubbing together 4 bits at a time to constitute a single entity of the system which is composed of 16 symbols including 10 digits ranging from 0-9 and the first six alphabets from A-F. The word Hexadecimal is derived from the words Hex which means six and decimal which means ten.
Thus the combined word denotes sixteen which is six and ten added together. The Hexadecimal Sequences are also referred to as the base or radix 16. While dealing with different Number Systems, it becomes essential to be able to convert them from one system to another. In this article, we focus on converting Hexadecimal to Binary, which is a system comprised of 1’s and 0’s and is the mechanism through which the computers store and process instructions as well as data.
Examples :
Hexadecimal Sequence : 458A
Binary Equivalent : 0100010110001010
Explanation : Binary representation of A : 1010
Binary representation of 8 : 1000
Binary representation of 5 : 0101
Binary representation of 4 : 0100
Hexadecimal Sequence : B36
Binary Equivalent : 101100110110
There are two approaches to convert Hexadecimal to Binary and they are mentioned as follows :
- Using the key-value pair for the corresponding conversion from the Hexadecimal character to its Binary equivalent
- Converting the Hexadecimal to its Decimal equivalent which is further converted to its Binary equivalent
Approach 1 :
Using this approach, we formulate key-value and extracting every character of the Hexadecimal string, add its corresponding binary sequence and return the complete binary sequence.
- Create a HashMap to store the key-value pairs.
- Accept the Hexadecimal sequence as a string and extract each character while iterating through the length of the string.
- Check if the extracted character is present in the keys of the HashMap.
- If it is present, concatenate the string storing the binary sequence with the corresponding value of the key.
- If it is not present, return Invalid Hexadecimal String.
Code:
Java
// Java program to convert Hexadecimal to Binaryimport java.util.HashMap;class GFG { // declaring the method to convert // Hexadecimal to Binary String hexToBinary(String hex) { // variable to store the converted // Binary Sequence String binary = ""; // converting the accepted Hexadecimal // string to upper case hex = hex.toUpperCase(); // initializing the HashMap class HashMap<Character, String> hashMap = new HashMap<Character, String>(); // storing the key value pairs hashMap.put('0', "0000"); hashMap.put('1', "0001"); hashMap.put('2', "0010"); hashMap.put('3', "0011"); hashMap.put('4', "0100"); hashMap.put('5', "0101"); hashMap.put('6', "0110"); hashMap.put('7', "0111"); hashMap.put('8', "1000"); hashMap.put('9', "1001"); hashMap.put('A', "1010"); hashMap.put('B', "1011"); hashMap.put('C', "1100"); hashMap.put('D', "1101"); hashMap.put('E', "1110"); hashMap.put('F', "1111"); int i; char ch; // loop to iterate through the length // of the Hexadecimal String for (i = 0; i < hex.length(); i++) { // extracting each character ch = hex.charAt(i); // checking if the character is // present in the keys if (hashMap.containsKey(ch)) // adding to the Binary Sequence // the corresponding value of // the key binary += hashMap.get(ch); // returning Invalid Hexadecimal // String if the character is // not present in the keys else { binary = "Invalid Hexadecimal String"; return binary; } } // returning the converted Binary return binary; } // Driver Code public static void main(String[] args) { // instantiating the class GFG ob = new GFG(); String hex = "deafa"; System.out.println(hex.toUpperCase()); // printing and calling the // hexToBinary() function System.out.println(ob.hexToBinary(hex)); }} |
DEAFA 11011110101011111010
Time complexity: O(n), where n is the length of the input Hexadecimal string.
Auxiliary space: O(n), where n is the length of the input Hexadecimal string.
Approach 2:
This approach first converts the Hexadecimal String into its decimal equivalent which is further converted into its binary equivalent. We make use of two functions, the first one to convert the Hexadecimal to Decimal and the second one to convert Decimal to Binary.
- First, we write the function to convert the Decimal to Binary.
- Next, we, write the function to convert Hexadecimal to Decimal and call the above function inside this function to convert the converted Decimal further into Binary.
- In this function, we iterate through the length of the Hexadecimal String and extract every character one at a time.
- Next, we check if the extracted characters are in the range 0-9 or A-F.
- If the characters are present in the above-mentioned range we concatenate them to the decimal string.
- Next, the decimal string is converted to Binary using the decimalToBinary() function.
- If even one of the characters is not present in the above-mentioned range, Invalid Hexadecimal String is returned as the output.
Below is the implementation of the above approach:
Java
// Java program to convert Hexadecimal to Binaryclass GFG { // method to convert Decimal to Binary String decimalToBinary(int decimal) { // variable to store the converted // binary string String binaryString = ""; // loop to generate the binary while (decimal != 0) { // concatenating the remainder // on dividing by 2 to the // binary string binaryString = (decimal % 2) + binaryString; // updating the decimal integer // by dividing by 2 in each iteration decimal /= 2; } // loop to ensure that each // Hexadecimal character is // represented by 4 bits while (binaryString.length() % 4 != 0) { // adding leading 0's if the // character is represented by less // than 4 bits binaryString = "0" + binaryString; } // returning the converted binary string return binaryString; } // method to convert Hexadecimal to Binary String hexToBinary(String hexadecimal) { // declaring the variables int i; char ch; String binary = ""; int returnedBinary; // converting the accepted Hexadecimal // String to upper case hexadecimal = hexadecimal.toUpperCase(); // loop to iterate through the length // of the Hexadecimal String for (i = 0; i < hexadecimal.length(); i++) { // extracting the characters ch = hexadecimal.charAt(i); // condition to check if // the character is not a valid Hexadecimal // character if (Character.isDigit(ch) == false && ((int)ch >= 65 && (int)ch <= 70) == false) { // returning Invalid Hexadecimal // String for the invalid Hexadecimal // character binary = "Invalid Hexadecimal String"; return binary; } // checking if the character is a valid // Hexadecimal alphabet else if ((int)ch >= 65 && (int)ch <= 70) // converting alphabet to // corresponding value such as 10 // for A and so on using ASCII code returnedBinary = (int)ch - 55; else returnedBinary = Integer.parseInt(String.valueOf(ch)); // converting the decimal to binary // by calling the decimalToBinary() method binary += decimalToBinary(returnedBinary); } // returning the converted binary sequence return binary; } // Driver Code public static void main(String[] args) { // instantiating the class GFG ob = new GFG(); String hex = "abcfde"; System.out.println(hex); // printing and calling the // hexToBinary() function to display the // output System.out.println(ob.hexToBinary(hex)); }} |
abcfde 101010111100111111011110
Time complexity: O(n*m)
Auxiliary space: O(nm)
