Program to Convert Hexadecimal Number to Binary

Last Updated : 29 Apr, 2023

Given a Hexadecimal number as an input, the task is to convert that number to a Binary number.
Examples:

Input: Hexadecimal = 1AC5
Output: Binary = 0001101011000101
Explanation:
    Equivalent binary value of 1: 0001
    Equivalent binary value of A: 1010
    Equivalent binary value of C: 1100
    Equivalent binary value of 5: 0101

Input: Hexadecimal = 5D1F
Output: Binary = 0101110100011111

Approach: A hexadecimal number is a positional numeral system with a radix, or base, of 16 and uses sixteen distinct symbols.
A binary number is a number expressed in the base-2 binary numeral system, which uses only two symbols: which are 0 (zero) and 1 (one).

To convert HexaDecimal number to Binary, the binary equivalent of each digit of the HexaDecimal number is evaluated and combined at the end to get the equivalent binary number.

Below is the implementation of the above approach:

C++

// C++ program to convert
// Hexadecimal number to Binary
 
#include <bits/stdc++.h>
using namespace std;
 
// function to convert
// Hexadecimal to Binary Number
void HexToBin(string hexdec)
{
      //Skips "0x" if present at beggining of Hex string
    size_t i = (hexdec[1] == 'x' || hexdec[1] == 'X')? 2 : 0;
 
    while (hexdec[i]) {
 
        switch (hexdec[i]) {
        case '0':
            cout << "0000";
            break;
        case '1':
            cout << "0001";
            break;
        case '2':
            cout << "0010";
            break;
        case '3':
            cout << "0011";
            break;
        case '4':
            cout << "0100";
            break;
        case '5':
            cout << "0101";
            break;
        case '6':
            cout << "0110";
            break;
        case '7':
            cout << "0111";
            break;
        case '8':
            cout << "1000";
            break;
        case '9':
            cout << "1001";
            break;
        case 'A':
        case 'a':
            cout << "1010";
            break;
        case 'B':
        case 'b':
            cout << "1011";
            break;
        case 'C':
        case 'c':
            cout << "1100";
            break;
        case 'D':
        case 'd':
            cout << "1101";
            break;
        case 'E':
        case 'e':
            cout << "1110";
            break;
        case 'F':
        case 'f':
            cout << "1111";
            break;
        case '.':
            cout << ".";
            break;
        default:
            cout << "\nInvalid hexadecimal digit "
                 << hexdec[i];
        }
        i++;
    }
}
 
// driver code
int main()
{
 
    // Get the Hexadecimal number
    char hexdec[100] = "1AC5";
 
    // Convert HexaDecimal to Binary
    cout << "\nEquivalent Binary value is : ";
    HexToBin(hexdec);
 
    return 0;
}

C

// C program to convert
// Hexadecimal number to Binary
 
#include <stdio.h>
 
// function to convert Hexadecimal to Binary Number
void HexToBin(char* hexdec)
{
 
    //Skips "0x" if present at beggining of Hex string
    size_t i = (hexdec[1] == 'x' || hexdec[1] == 'X')? 2 : 0;
 
    while (hexdec[i]) {
 
        switch (hexdec[i]) {
        case '0':
            printf("0000");
            break;
        case '1':
            printf("0001");
            break;
        case '2':
            printf("0010");
            break;
        case '3':
            printf("0011");
            break;
        case '4':
            printf("0100");
            break;
        case '5':
            printf("0101");
            break;
        case '6':
            printf("0110");
            break;
        case '7':
            printf("0111");
            break;
        case '8':
            printf("1000");
            break;
        case '9':
            printf("1001");
            break;
        case 'A':
        case 'a':
            printf("1010");
            break;
        case 'B':
        case 'b':
            printf("1011");
            break;
        case 'C':
        case 'c':
            printf("1100");
            break;
        case 'D':
        case 'd':
            printf("1101");
            break;
        case 'E':
        case 'e':
            printf("1110");
            break;
        case 'F':
        case 'f':
            printf("1111");
            break;
        case '.':
            printf(".");
        default:
            printf("\nInvalid hexadecimal digit %c",
                   hexdec[i]);
        }
        i++;
    }
}
 
// driver code
int main()
{
 
    // Get the Hexadecimal number
    char hexdec[100] = "1AC5";
 
    // Convert HexaDecimal to Binary
    printf("\nEquivalent Binary value is : ");
    HexToBin(hexdec);
}

Java

// Java program to convert
// Hexadecimal number to Binary
 
public class Improve {
 
    // function to convert
    // Hexadecimal to Binary Number
    static void HexToBin(char hexdec[])
    {
        int i = 0;
 
        while (hexdec[i] != '\u0000') {
 
            switch (hexdec[i]) {
            case '0':
                System.out.print("0000");
                break;
            case '1':
                System.out.print("0001");
                break;
            case '2':
                System.out.print("0010");
                break;
            case '3':
                System.out.print("0011");
                break;
            case '4':
                System.out.print("0100");
                break;
            case '5':
                System.out.print("0101");
                break;
            case '6':
                System.out.print("0110");
                break;
            case '7':
                System.out.print("0111");
                break;
            case '8':
                System.out.print("1000");
                break;
            case '9':
                System.out.print("1001");
                break;
            case 'A':
            case 'a':
                System.out.print("1010");
                break;
            case 'B':
            case 'b':
                System.out.print("1011");
                break;
            case 'C':
            case 'c':
                System.out.print("1100");
                break;
            case 'D':
            case 'd':
                System.out.print("1101");
                break;
            case 'E':
            case 'e':
                System.out.print("1110");
                break;
            case 'F':
            case 'f':
                System.out.print("1111");
            case '.':
                System.out.print(".");
                break;
            default:
                System.out.print("\nInvalid hexadecimal digit " + hexdec[i]);
            }
            i++;
        }
    }
 
    // Driver code
    public static void main(String args[])
    {
        // Get the Hexadecimal number
        String s = "1AC5" ;
        char hexdec[] = new char[100] ;
            hexdec = s.toCharArray() ;
 
        // Convert HexaDecimal to Binary
        System.out.print("\nEquivalent Binary value is : ");
        try{
            HexToBin(hexdec);
        }
        catch (ArrayIndexOutOfBoundsException e){
            System.out.print("");
        }
 
    }
    // This code is contributed by ANKITRAI1
}

Python3

# Python3 program to convert
# Hexadecimal number to Binary
 
# Function to convert
# Hexadecimal to Binary Number
def HexToBin(hexdec):
  
    for i in hexdec:        
        if i == '0':
            print('0000', end = '')
        elif i == '1':
            print('0001', end = '')
        elif i == '2':
            print('0010', end = '')
        elif i == '3':
            print('0011', end = '')
        elif i == '4':
            print('0100', end = '')
        elif i == '5':
            print('0101', end = '')
        elif i == '6':
            print('0110', end = '')
        elif i == '7':
            print('0111', end = '')
        elif i == '8':
            print('1000', end = '')
        elif i == '9':
            print('1001', end = '')
        elif i == 'A' or i == 'a':
            print('1010', end = '')
        elif i == 'B' or i == 'b':
            print('1011', end = '')
        elif i == 'C' or i == 'c':
            print('1100', end = '')
        elif i == 'D' or i == 'd':
            print('1101', end = '')
        elif i == 'E' or i == 'e':
            print('1110', end = '')
        elif i == 'F' or i == 'f':
            print('1111', end = '')
        elif i == '.':
              print('.', end = '')
        else:
            print("\nInvalid hexadecimal digit " +
                    str(hexdec[i]), end = '')
             
# Driver code
if __name__=="__main__":
     
    # Get the Hexadecimal number
    hexdec= "1AC5";
  
    # Convert HexaDecimal to Binary
    print("Equivalent Binary value is : ",
           end = '')
    HexToBin(hexdec)
     
# This code is contributed by Rutvik_56

C#

// C# program to convert Hexadecimal 
// number to Binary
 
class GFG 
{
 
// function to convert
// Hexadecimal to Binary Number
static void HexToBin(char[] hexdec)
{
int i = 0;
 
while (hexdec[i] != '\u0000') 
{
 
    switch (hexdec[i]) 
    {
    case '0':
        System.Console.Write("0000");
        break;
    case '1':
        System.Console.Write("0001");
        break;
    case '2':
        System.Console.Write("0010");
        break;
    case '3':
        System.Console.Write("0011");
        break;
    case '4':
        System.Console.Write("0100");
        break;
    case '5':
        System.Console.Write("0101");
        break;
    case '6':
        System.Console.Write("0110");
        break;
    case '7':
        System.Console.Write("0111");
        break;
    case '8':
        System.Console.Write("1000");
        break;
    case '9':
        System.Console.Write("1001");
        break;
    case 'A':
    case 'a':
        System.Console.Write("1010");
        break;
    case 'B':
    case 'b':
        System.Console.Write("1011");
        break;
    case 'C':
    case 'c':
        System.Console.Write("1100");
        break;
    case 'D':
    case 'd':
        System.Console.Write("1101");
        break;
    case 'E':
    case 'e':
        System.Console.Write("1110");
        break;
    case 'F':
    case 'f':
        System.Console.Write("1111");
        break;
    case '.':
        System.Console.Write('.');
        break;
    default:
        System.Console.Write("\nInvalid hexadecimal digit " + 
                                                  hexdec[i]);
        break;
    }
    i++;
}
}
 
// Driver code
static void Main()
{
    // Get the Hexadecimal number
    string s = "1AC5" ;
    char[] hexdec = new char[100];
           hexdec = s.ToCharArray();
 
    // Convert HexaDecimal to Binary
    System.Console.Write("Equivalent Binary value is : ");
    try
    {
        HexToBin(hexdec);
    }
    catch (System.IndexOutOfRangeException)
    {
        System.Console.Write("");
    }
}
}
 
// This code is contributed by mits

PHP

<?php
// PHP program to convert
// Hexadecimal number to Binary
 
// function to convert
// Hexadecimal to Binary Number
function HexToBin($hexdec)
{
    $i = 0;
     
    while ($hexdec[$i])
    {
        switch ($hexdec[$i])
        {
        case '0':
            echo "0000";
            break;
        case '1':
            echo "0001";
            break;
        case '2':
            echo "0010";
            break;
        case '3':
            echo "0011";
            break;
        case '4':
            echo "0100";
            break;
        case '5':
            echo "0101";
            break;
        case '6':
            echo "0110";
            break;
        case '7':
            echo "0111";
            break;
        case '8':
            echo "1000";
            break;
        case '9':
            echo "1001";
            break;
        case 'A':
        case 'a':
            echo "1010";
            break;
        case 'B':
        case 'b':
            echo "1011";
            break;
        case 'C':
        case 'c':
            echo "1100";
            break;
        case 'D':
        case 'd':
            echo "1101";
            break;
        case 'E':
        case 'e':
            echo "1110";
            break;
        case 'F':
        case 'f':
            echo "1111";
            break;
        case '.':
            echo ".";
            break;
        default:
            echo "\nInvalid hexadecimal digit ".
                                    $hexdec[$i];
        }
        $i++;
    }
}
 
// Driver Code
 
// Get the Hexadecimal number
$hexdec = "1AC5";
 
// Convert HexaDecimal to Binary
echo "\nEquivalent Binary value is : ";
HexToBin($hexdec);
 
// This code is contributed 
// by Akanksha Rai

Javascript

<script>
// JavaScript program to convert
// Hexadecimal number to Binary
 
// function to convert
// Hexadecimal to Binary Number
function HexToBin(hexdec)
{
    var i = 0;
 
    while (hexdec[i]) {
 
        switch (hexdec[i]) {
        case '0':
            document.write("0000");
            break;
        case '1':
            document.write("0001");
            break;
        case '2':
            document.write("0010");
            break;
        case '3':
            document.write("0011");
            break;
        case '4':
           document.write("0100");
            break;
        case '5':
            document.write("0101");
            break;
        case '6':
            document.write("0110");
            break;
        case '7':
            document.write("0111");
            break;
        case '8':
            document.write("1000");
            break;
        case '9':
            document.write("1001");
            break;
        case 'A':
        case 'a':
            document.write("1010");
            break;
        case 'B':
        case 'b':
            document.write("1011");
            break;
        case 'C':
        case 'c':
            document.write("1100");
            break;
        case 'D':
        case 'd':
            document.write("1101");
            break;
        case 'E':
        case 'e':
            document.write("1110");
            break;
        case 'F':
        case 'f':
            document.write("1111");
            break;
        case '.': 
            document.write(".");
            break;
        default:
            document.write("\nInvalid hexadecimal digit " + hexdec[i]);
        }
        i++;
    }
}
 
// driver code
// Get the Hexadecimal number
var hexdec = "1AC5";
 
// Convert HexaDecimal to Binary
document.write("\nEquivalent Binary value is : ");
HexToBin(hexdec);
 
// This code is contributed by phasing17
</script>

Output:

Equivalent Binary value is : 0001101011000101

Time Complexity: O(n)

Auxiliary Space: O(1)

Alternate Approach :

C++

#include <bits/stdc++.h>
using namespace std;
 
string hexToBinary(string input)
{
  /*Using stoul() to get the decimal value
         * of the given String*/
  unsigned int x =  stoul(input, nullptr, 16) ;
 
 
  /*Using bitset<16>(x).to_string() to get the binary
         * String of given integer*/
  string result = bitset<16>(x).to_string(); 
 
  /*Alternatively you may also merge above operations
        to one line like
        * string result = bitset<16>(stoul(input, nullptr, 16)).to_string();
          */
  return result;
}
int main() {
 
  string s = "1AC5";
  string result = hexToBinary(s);
  cout << result;
  return 0;
}
 
// This code is contributed by abhijeet1904.

Java

/*package whatever //do not write package name here */
 
import java.io.*;
 
class HexToBinary {
    public static void main(String[] args)
    {
        String s = "1AC5";
        String result = hexToBinary(s);
        System.out.println(result);
    }
    private static String hexToBinary(String input)
    {
        /*Using Integer.parseInt() to get the decimal value
         * of the given String*/
        int decimalValue = Integer.parseInt(input, 16);
 
        /*Using Integer.toBinaryString() to get the binary
         * String of given integer*/
        String result
            = Integer.toBinaryString(decimalValue);
 
        /*Alternatively you may also merge above operations
        to one line like
        * String result = Integer.toBinaryString(Integer.parseInt(input, 16));
          */
        return result;
    }
}

Python

# Python3 program to convert
# Hexadecimal number to Binary
 
def to4DigitBin(value):
 
    # Converts given binary value into 4-digit 
    # Binary representation.
    # If given value is '10', it returns '0010'
    # i.e. 2 times '0' + '10'='00'+'10'
    return '0'*(4-len(value))+value
  
def HexadecimalToBinary(inputHexadecimal):
    resultBinary = '' # Initialize Empty string
  
    for eachElement in inputHexadecimal:
 
        # If it's a number digit (in 0 to 9), find it's binary form.
        if(eachElement.isdigit()):
 
            # Here bin(number) function returns Binary 
            # representation of number
            # Ex: bin(10) returns '0b1010', so slice away
            # the first 2 characters to get '1010'
            binaryOfSingleDigit = bin(int(eachElement))[2:]
  
            # Now add the 4-digit Binary representation to 
            # result string
            resultBinary += to4DigitBin(binaryOfSingleDigit)
 
        # Since the element is alphabet (in A to E), (assuming 
        # only capital letters)
        # 'ord(element)-65+10' gives the number representation 
        # ranging 10 to 16 (for A to E)
        # Ex: For 'B', ord('B')=66, thus 'ord('B')-65+10' => '
        # 66-65+10' => '11'
        elif(eachElement.isalpha() and ord(eachElement) < 71):
            resultBinary += to4DigitBin(bin(ord(eachElement)-55)[2:])
 
        # If invalid character is present  
        else:            
            resultBinary = 'Invalid hexadecimal digit: ' + eachElement
            break
  
    return 'Equivalent Binary value is: '+ resultBinary
  
# Driver code
inputHexadecimal = '1AC5'   # input('Enter Hexadecimal: ')
print(HexadecimalToBinary(inputHexadecimal))
  
# This code is contributed by SBVKrishna

C#

// C# program to implement the approach
using System;
 
class HexToBinary {
 
  // Driver Code
  public static void Main(string[] args)
  {
    string s = "1AC5";
    string result = hexToBinary(s);
 
    // Function Call
    Console.WriteLine(result);
  }
 
  // Function to convert hex string to binary string
  private static string hexToBinary(string input)
  {
    // Convert the hex string to decimal integer
    int decimalValue = Convert.ToInt32(input, 16);
 
    // Convert the decimal value to binary string
    string result = Convert.ToString(decimalValue, 2);
 
    return result;
  }
}
 
// This code is contributed by phasing17

Javascript

// JS Program to implement the approach
 
function hexToBinary(input)
{
    /*Using parseInt to get the decimal value
     of the given String*/
    var decimalValue = parseInt(input, 16);
 
    /*Using decimalValue to get the binary
    * String of given integer*/
    var result = decimalValue.toString(2);
     
    /* Calculating the length of the binary number
    with leading zeroes */
    var len = 4 * (Math.floor(result.length / 4) + (result.length % 4 ? 1 : 0));
     
    return result.padStart(len, '0');
}
 
// Driver Code
var s = "1AC5";
var result = hexToBinary(s);
console.log(result);
console.log("0001101011000101");
 
// This code is contributed by phasing17

Output

Equivalent Binary value is: 0001101011000101

Time Complexity: O(1)

Auxiliary Space: O(1)

Method 3: Manual Conversion

1. The function first defines a dictionary called hex_to_bin_dict, which maps each hexadecimal digit to its binary representation. This is done using a series of key-value pairs in the format ‘hex_digit’: ‘binary_digit’.

2. The input hexadecimal number is converted to uppercase using the upper() method to avoid issues with lowercase letters.

3. The function then creates an empty string called bin_num, which will be used to store the binary representation of the input hexadecimal number.

4. For each digit in the input hexadecimal number, the corresponding binary digit is retrieved from the hex_to_bin_dict dictionary using square bracket notation, and added to the bin_num string. This process is repeated for each digit in the input hexadecimal number.

Finally, the function returns the binary representation of the input hexadecimal number as a string.

Python3

def hex_to_bin(hex_num):
    hex_to_bin_dict = {
        '0': '0000', '1': '0001', '2': '0010', '3': '0011',
        '4': '0100', '5': '0101', '6': '0110', '7': '0111',
        '8': '1000', '9': '1001', 'A': '1010', 'B': '1011',
        'C': '1100', 'D': '1101', 'E': '1110', 'F': '1111'
    }
 
    hex_num = hex_num.upper()
    bin_num = ''
    for digit in hex_num:
        bin_num += hex_to_bin_dict[digit]
    return bin_num
hex_num = "1AC5"
print(hex_to_bin(hex_num))

Java

public class HexToBin {
    public static void main(String[] args) {
        String hex_num = "1AC5";
        String bin_num = hexToBin(hex_num);
        System.out.println(bin_num);
    }
 
    public static String hexToBin(String hex_num) {
        hex_num = hex_num.toUpperCase();
        String hex_to_bin_dict[] = {
                "0000", "0001", "0010", "0011",
                "0100", "0101", "0110", "0111",
                "1000", "1001", "1010", "1011",
                "1100", "1101", "1110", "1111"
        };
        String bin_num = "";
        for (int i = 0; i < hex_num.length(); i++) {
            bin_num += hex_to_bin_dict[Character.digit(hex_num.charAt(i), 16)];
        }
        return bin_num;
    }
}

C++

#include <iostream>
#include <string>
#include <unordered_map>
 
std::string hex_to_bin(std::string hex_num) {
    std::unordered_map<char, std::string> hex_to_bin_dict {
        {'0', "0000"}, {'1', "0001"}, {'2', "0010"}, {'3', "0011"},
        {'4', "0100"}, {'5', "0101"}, {'6', "0110"}, {'7', "0111"},
        {'8', "1000"}, {'9', "1001"}, {'A', "1010"}, {'B', "1011"},
        {'C', "1100"}, {'D', "1101"}, {'E', "1110"}, {'F', "1111"}
    };
 
    std::string bin_num;
    for (char digit : hex_num) {
        bin_num += hex_to_bin_dict[std::toupper(digit)];
    }
    return bin_num;
}
 
int main() {
    std::string hex_num = "1AC5";
    std::cout << hex_to_bin(hex_num) << std::endl;
    return 0;
}

C#

using System;
using System.Collections.Generic;
 
class Program {
    static string HexToBin(string hexNum) {
        Dictionary<char, string> hexToBinDict = new Dictionary<char, string>() {
            {'0', "0000"}, {'1', "0001"}, {'2', "0010"}, {'3', "0011"},
            {'4', "0100"}, {'5', "0101"}, {'6', "0110"}, {'7', "0111"},
            {'8', "1000"}, {'9', "1001"}, {'A', "1010"}, {'B', "1011"},
            {'C', "1100"}, {'D', "1101"}, {'E', "1110"}, {'F', "1111"}
        };
 
        string binNum = "";
        foreach (char digit in hexNum.ToUpper()) {
            binNum += hexToBinDict[digit];
        }
        return binNum;
    }
 
    static void Main(string[] args) {
        string hexNum = "1AC5";
        Console.WriteLine(HexToBin(hexNum));
    }
}

Javascript

// JavaScript program for the above approach
function hexToBin(hexNum) {
    // Mapping of hexadecimal to binary
    const hexToBinDict = {
    '0': '0000', '1': '0001', '2': '0010', '3': '0011',
    '4': '0100', '5': '0101', '6': '0110', '7': '0111',
    '8': '1000', '9': '1001', 'A': '1010', 'B': '1011',
    'C': '1100', 'D': '1101', 'E': '1110', 'F': '1111'
    };
     
    // Convert the hexadecimal string to uppercase
    hexNum = hexNum.toUpperCase();
     
    // Initialize the binary string
    let binNum = '';
     
    // Iterate through each digit in the hexadecimal string
    for (let i = 0; i < hexNum.length; i++) {
        const digit = hexNum[i];
        // Append the binary representation of the current digit to the binary string
        binNum += hexToBinDict[digit];
    }
     
    // Return the binary string
    return binNum;
}
 
const hexNum = "1AC5";
console.log(hexToBin(hexNum));
 
// This code is contributed by phasing17

Output

0001101011000101

Time complexity: O(n)
Auxiliary space: O(n)

Program to convert a Binary Number to Hexa-Decimal Number

Kanishk_Verma

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