## Thursday, August 20, 2015

### Converting from Base 12 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert A245A3B12 into Base 10.

Solution:

The given number which is
A245A3B12 is written in Base 12. Base 12 number is also called duodecimal system. The digits of Base 12 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. Since 10 and 11 are not accepted as a digit, then we have to substitute a variable which is A = 10 and B = 11. Hence, the digits of a Base 12 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B.

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
A245A3B12 into Base 10. How? Let's multiply each digits by the powers of 12 as follows:

Base 6 Digits:
A      2      4      5      A      3      B
Multiply by:
12⁶   12⁵   12⁴   12³   12²   12¹   12

Add all the digits, we have

(A x 12⁶) + (2 x 12⁵) + (4 x 12⁴) + (5 x 12³) + (A x 12²) + (3 x 12¹) + (B x 12) = 29859840 + 497664 + 82944 + 8640 + 1440 + 36 + 11 = 30450575

Therefore,
A245A3B12 = 30450575