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

Thursday, August 27, 2015

Converting from Base 14 to Base 10 Problems

Category: Arithmetic

"Published in Newark, California, USA"

Convert 15DC214 into Base 10.

Solution:

The given number which is
15DC214 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
15DC214 into Base 10. How? Let's multiply each digits by the powers of 14 as follows:

Base 6 Digits:        1      5       D      C      2

Multiply by:
14⁴   14³    14²   14¹   14

Add all the digits, we have

(1 x 14⁴) + (5 x 14³) + (D x 14²) + (C x 14¹) + (2 x 14) = 38416 + 13720 + 2548 + 168 + 2 = 54854

Therefore,
15DC214 = 54854

Wednesday, August 26, 2015

Converting from Base 10 to Base 14 Problems, 2

Category: Arithmetic

"Published in Newark, California, USA"

Convert 6995483 into Base 14.

Solution:

The given number which is
6995483 is written in Base 10. 6995483 can also be written as 699548310. 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.  The digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10 number is a common number that we are using right now in everyday life.

On the other hand, Base 14 number is a number whose digits 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 single digit, then we have to use a variable to substitute a two digit number. In this case, let A = 10, B = 11, C = 12, and D = 13. Hence, the digits of Base 14 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, and D. If you see a subscript of 14 at the given number, then that number is written in Base 14. Base 14 number is also called tetradecimal system.

Now, let's convert
6995483 into Base 14. How? Let's divide 6995483 by 14 as follows:

6995483 ÷ 14 = 499677 + R(5)

Next, let's divide the quotient, which is 499677, as follows:

6995483 ÷ 14 = 499677 + R(5)
499677 ÷ 14 =   35691 + R(3)

Do the same thing with 35691 until the quotient is 0 as follows:

6995483 ÷ 14 = 499677 + R(5)
499677 ÷ 14 =   35691 + R(3)

35691 ÷ 14 =     2549 + R(5)
2549 ÷ 14 =       182 + R(1)
182 ÷ 14 =         13 + R(0)
13 ÷ 14 =           0 + R(13 or D)

The remainders will be the digits of Base 14 number. Use the digits of the remainders from bottom to top. Therefore,

6995483
= D0153514