__Category__: Arithmetic"Published in Newark, California, USA"

Convert 1A0BDC2

_{14}into Base 10.

__Solution__:

The given number which is 1A0BDC2

_{14}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 1A0BDC2

_{14}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: 14⁶ 14⁵ 14⁴ 14³ 14² 14¹ 14⁰

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 14⁰) = 7529536 + 5378240 + 0 + 30184 + 2548 + 168 + 2 = 12940678

Therefore, 1A0BDC2

_{14}=

**12940678**