Decimal 2 Decimal Transforming Numerical Systems

Lesson 5: Decimal 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 exampleswhere both X & Y equal to 10 (decimal base, B=10)

Decimal System:

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


Example

Transform 5324 (decimal) into decimal number (?!) using method of continuous dividing – result 5324

5324 : 10 = 532 , remaining 4 100 last digit
532 : 10 = 53 , remaining 2 101
53 : 10 = 5 , remaining 3 102
5 : 10 = 0 , remaining 5 103 first digit

- end of procedure


Example

Transform 0,8125 (decimal) into decimal number (?!) using method of continuous multiplying – result 0,8125

0,8125 * 10 = 8, 125 10-1 first digit after zero
0,125 * 10 = 1, 25 10-2
0,25 * 10 = 2, 5 10-3
0,5 * 10 = 5, 0 10-4 last digit

0,0 end of procedure