Hexadecimal 2 Decimal Transforming Numerical Systems

Lesson 6: Hexadecimal 2 Decimal

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 = 16 (source is hex base, B1=16) and Y = 10 (destination is decimal base, B2=10).

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 System:

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

Hex 2 Decimal


Example

Transform 9EC,570A3 (hex) into decimal number

9EC, 570A3 16 = 9*162 + 14*161 + 12*160 + 5*16-1 + 7*16-2 + 0*16-3 + 10*16-4 + 3*16-5

 = 2304 + 224 +12 + 0,3125 + 0,02734375 + 0,0001525878... + 0,00000286102...

 = 2540 , 33999919891357421875