Hexadecimal to Binary Conversion

The number system conversion from hexadecimal number to binary number is explained by algorithm steps and it is tested by C programming implementation.

Hexadecimal number system

The hexadecimal number system has the following unique digits.
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f}

As the hexadecimal number system has the 16 unique digits, it is called base 16 or radix 16 number system.

Each hexadecimal digit can be represented by binary 4 bits, therefore the hexadecimal numbers helps remember long binary sequence.

Binary number system

The Binary number system has the following unique digits.
{0, 1}

As the binary number system has the 2 unique digits, it is called base 2 or radix 2 number system.

The computer can only understand or is operated by binary number system, therefore it accepts data,instruction and everything in binary numbers format.

Hexadecimal to Binary conversion example

The given hexadecima number is A06F and converts it into binary numbers

hexadecimal = A06F , binary = ?

1. split each digit of hexadecimal number
2. convert each hexadecimal digits into equivalent decimal number
3. carried out decimal to 4 bits binary conversion on each decimal number

       Hexa     =     A     |  0     |  6    |  F
       Decimal  =    10     |  0     |  6    |  15
    
       binary   =   1010  | 0000 |  0110 | 1111
 

if Hexadecimal value = 0xA06F and equivalent binary = 1010000001101111

Hexadecimal to Binary - C program

The number system conversion from hexadecimal number to binary number process implemented by C programming code and tested the results by giving a sample hexadecimal value.

 

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<stdlib.h>


char* dec2bin(int decval) {

    int n=0;  int bph=4;
    char *bits=(char*) malloc(sizeof(char)*bph+1);    
    for(int n=0;n<bph;n++)   
     {     
        int reminder= decval %2;
        decval  = decval /2;       
       bits[bph-n-1] = (reminder==1) ? '1' : '0';        
    }  
   bits[bph] = '\0';  
   return bits;
 }

int hex2dec(char hx) {

   int decval=0;
   
   switch (hx) 
    {   
  case '1' :
     decval=1;
  break;
  case '2':
     decval=2;
  break;
 case '3':
     decval=3;
  break;
 case '4':
     decval=4;
  break;
 case '5':
     decval=5;
  break;
 case '6':
     decval=6;
  break;
 case '7':
     decval=7;
  break;    
  case '8':
     decval=8;
  break;
  case '9':
     decval=9;
  break;
 case 'A':
 case 'a':
     decval=10;
  break;
 case 'B':
 case 'b':
     decval=11;
  break;
 case 'C':
 case 'c':
     decval=12;
  break;
 case 'D':
 case 'd':
     decval=13;
  break;
 case 'E':
 case 'e':
     decval=14;
  break;
 case 'F':
 case 'f':
     decval=15;
  break;
 default:
        decval =0;  
 }
 
 return decval;
   
}

int main() {

   int maxhex=5; 
   char hex[maxhex+1]; 
   char *bits;
   
   printf("\n Hexadecimal to Binary Conversion");
   
   printf("\n Enter hexadecimal value :") ;
   scanf("%s",&hex);
   
   for(int n=0;n<strlen(hex);n++) {
   
      int decval = hex2dec(hex[n]);   
      char *b4s = dec2bin(decval);
   strcat(bits,b4s);
   //printf("\n %c \t %d \t %s",hex[n],decval,dec2bin(decval));
   
   }
   
   printf("\nHexadecimal value : %s", hex); 
   printf("\nBinary bits       : %s ",bits);
   return 0;
}

 

Hexadecimal to Binary conversion - C program output

Hexadecimal to Binary Conversion
 Enter hexadecimal value :a4c5

Hexadecimal value : a4c5
Binary bits       :0000010000000101

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Download c program source code

• Hexadecimal to binary