**Decimal Number System: **

It is base 10 number system which uses the digits from 0 to 9.

**Hexadecimal Number System:**

It is base 16 number system which uses the digits from 0 to 9 and A, B, C, D, E, F.

### Logic to Convert Decimal to Hexadecimal C++:

- Divide the original decimal number by 16.
- Divide the quotient by 16.
- Repeat the step 2 until we get quotient equal to zero.
- Equivalent Hexadecimal number would be the remainders of each step in the reverse order.

#### Download Source Code:

Download: dectohex.cpp

## PROGRAM:

#include<iostream> using namespace std; int main() { long int decimalNumber,remainder,quotient; int i=1,j,temp; char hexadecimalNumber[100]; cout<<"Enter any decimal number: "; cin>>decimalNumber; quotient = decimalNumber; while(quotient!=0) { temp = quotient % 16; //To convert integer into character if( temp < 10) temp =temp + 48; else temp = temp + 55; hexadecimalNumber[i++]= temp; quotient = quotient / 16; } cout<<"nEquivalent hexadecimal number of "<<decimalNumber<<" is : "; for(j = i -1 ;j> 0;j--) cout<<hexadecimalNumber[j]; cout<<endl; return 0; }

### How Code Works:

Let user enter 900.

- 900 / 16 Remainder : 4 , Quotient : 56
- 56 / 16 Remainder : 8 , Quotient : 3
- 3 / 16 Remainder : 3 , Quotient : 0

Now Hexadecimal Number is remainders in each step in reverse order i.e. 384

Hence, hexadecimal equivalent of 900 is 384.

can you explain this part of the code?

while(quotient!=0)

{

temp = quotient % 16;

//To convert integer into character

if( temp < 10)

temp =temp + 48;

else

temp = temp + 55;

hexadecimalNumber[i++]= temp;

quotient = quotient / 16;

}

In ASCII there is a gap in the table between numbers 0-9 and the letters A-Z. The decimal number is being changed to char, however the ASCII decimal value of 0 is equal to [NULL]. By adding 48 when the entry is less than 10, < 10, you get the char value for the decimal entry. EX| if your entry is 3, 3+48 gives you the ASCII char value for the number 3. When the decimal number is greater than 10, in hexadecimal the value is a letter A-F. The conversion of temp + 55 simply assigns the char value of the corresponding number. EX| 10 = A in hex so, 10 + 55 gives the char value A. This is all because of conversions from integers to char relate to the ASCII table. My suggestion is that you find a table and go through the code, converting integer to char and so on, this should help you understand that conversion.