## Saturday, August 15, 2015

### Converting from Base 11 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 12A3A11 into Base 10.

Solution:

The given number which is
12A3A11 is written in Base 11. Base 11 number is also called undecimal system. The digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since 10 is not accepted as a digit, then we have to substitute a variable which is A = 10. Hence, the digits of a Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A.

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
12A3A11 into Base 10. How? Let's multiply each digits by the powers of 11 as follows:

Base 6 Digits:        1      2      A      3      A

Multiply by:
11⁴   11³    11²   11¹   11

Add all the digits, we have

(1 x 11⁴) + (2 x 11³) + (A x 11²) + (3 x 11¹) + (A x 11) = 14641 + 2662 + 1210 + 33 + 10 = 18556

Therefore,
12A3A11 = 18556