Numbers without Fractional Part :
- Division Method is used to convert such numbers from base 10 to another base
- The division is performed with the required base
Steps To Convert From Base 10 to Base 16
- Divide the given number (in base 10) with 16 until the result finally left is less than 16
- Traverse the remainders from bottom to top to get the required number in base 16
Numbers with Fractional Part :
- To convert such numbers from base 10 to another base, real part and fractional part are treated separately
- For Real Part :
- The steps involved in converting the real part from base 10 to another base are same as above.
- For Fractional Part :
- Multiplication Method is used to convert fractional part from base 10 to another base.
- The multiplication is performed with the required base
- For Real Part :
Example 1 (Real Number):
5815\(_{10}\) → (?)\(_{16}\)
Steps :
- 5815 / 16 = 363.4375 Fractional Part Separated 0.4375 * 16 = 7 or use mod operation (5815 mod 16 = 7)
- 363 / 16 = 22 → Reminder → 11 (which is “B” in Hexadecimal)
- 22 / 16 = 1 → Reminder → 6
- 1 / 16 = 0 → Reminder → 1
- Result is 16B7\(_{16}\)
Example 2 (Real Number with Fractional Part):
- 5815.65625\(_{10}\) → (16B7.?)\(_{16}\)
- Real Part Result is 16B7\(_{16}\)
Fractional Part :
- 0.65625 * 16 = 10.5 (10 in hexadecimal is “A”)
- 0.5 * 16 = 8
- Result is A8
Final Result is 16B7.A8\(_{16}\)
Informative : ASCII to Hex Table and Modulo Calculator