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”,”
b) right from “,”
Final result ~ 9EC , 570A316
Technorati Tags: Numeric, Numerical, Transform, Transformation, Binary, Decimal, Octal, Hexadecimal, Hex, Base, Complement, Method
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
Technorati Tags: Numeric, Numerical, Transform, Transformation, Binary, Decimal, Octal, Hexadecimal, Hex, Base, Complement, Method
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