Sunday, August 23, 2015

Converting from Base 13 to Base 10 Problems

Category: Arithmetic

"Published in Newark, California, USA"

Convert A12BC13 into Base 10.

Solution:

The given number which is
A12BC13 is written in Base 13. Base 13 number is also called tridecimal system. The digits of Base 13 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Since 10, 11, and 12 are not accepted as a digit, then we have to substitute a variable which is A = 10, B = 11, and C = 12. Hence, the digits of a Base 13 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C.

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
A12BC13 into Base 10. How? Let's multiply each digits by the powers of 13 as follows:

Base 6 Digits:        A      1       2      B      C

Multiply by:
13⁴   13³    13²   13¹   13

Add all the digits, we have

(A x 13⁴) + (1 x 13³) + (2 x 13²) + (B x 13¹) + (C x 13) = 285610 + 2197 + 338 + 143 + 12 = 288300

Therefore,
A12BC13 = 288300