Decimal 2 Hexadecimal Transforming Numerical Systems

 Lesson 4: Decimal 2 Hexadecimal

Number we want to transform uses base X: we would like to transform this number into new one, that uses Y base. In this case we will use method of continuous dividing and multiplying (dividing numbers left of comma (,) with Y and multiplying numbers on the right side of comma, by Y - rational numbers). This method is best understood looking at these examples, where X equals 10 and Y equals 16 ( hex base, B=16)


Decimal System:

Base: 10
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9


Hexadecimal (hex) System:

Base: 16
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Example: 27 (decimal) = 1B ₁₆ (hex)


Decimal 2 Hex

Example

Transform 2540,34 (decimal) into hex number-result ~ 9EC, 570A3₁₆

a) left from”,”

2540 : 16 = 158 , remaining 12 => C 160 last digit
158 : 16 = 9 , remaining 14 => E 161
 9 : 16 = 0 , remaining 9 => 9  162 first digit

end of procedure => 9EC 16

b) right from ",”

0,34 * 16 = 5,44 5 => 5 16-1 first digit after zero
0,44 * 16 = 7,04 7 => 7 16-2
0,04 * 16 = 0,64 0 => 0 16-3
0,64 * 16 = 10,24 10 =>  A 16-4
0,24 * 16 = 3,84 3 => 3 16-5 
…
…
procedure could be continued => 0, 570A3… 16

Final result ~ 9EC , 570A3₁₆