## Friday, August 28, 2015

### Converting from Base 14 to Base 10 Problems, 2

Category: Arithmetic

"Published in Newark, California, USA"

Convert 1A0BDC214 into Base 10.

Solution:

The given number which is
1A0BDC214 is written in Base 14. Base 14 number is also called tetradecimal system. The digits of Base 14 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13. Since 10, 11, 12, and 13 are not accepted as a digit, then we have to substitute a variable which is A = 10, B = 11, C = 12, and D = 13. Hence, the digits of a Base 14 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, and D.

On the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system. Base 10 number is a common number that we are using right now in everyday life.

Now, let's convert
1A0BDC214 into Base 10. How? Let's multiply each digits by the powers of 14 as follows:

Base 6 Digits:       1
A      0     B      D      C      2
Multiply by:
14⁶   14⁵   14⁴   14³   14²   14¹   14

Add all the digits, we have

(1 x 14⁶) + (A x 14⁵) + (0 x 14⁴) + (B x 14³) + (D x 14²) + (C x 14¹) + (2 x 14) = 7529536 + 5378240 + 0 + 30184 + 2548 + 168 + 2 = 12940678

Therefore,
1A0BDC214 = 12940678