## Tuesday, August 25, 2015

### Converting from Base 10 to Base 14 Problems

Category: Arithmetic

"Published in Newark, California, USA"

Convert 74569 into Base 14.

Solution:

The given number which is
74569 is written in Base 10. 74569 can also be written as 7456910. 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
74569 into Base 14. How? Let's divide 74569 by 14 as follows:

74569 ÷ 14 = 5326 + R(5)

Next, let's divide the quotient, which is 5326, as follows:

74569 ÷ 14 = 5326 + R(5)
5326 ÷ 14 =   380 + R(6)

Do the same thing with 380 until the quotient is 0 as follows:

74569 ÷ 14 = 5326 + R(5)
5326 ÷ 14 =   380 + R(6)

380 ÷ 14 =     27 + R(2)
27 ÷ 14 =       1 + R(13 or D)
1 ÷ 14 =       0 + R(1)

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

74569
= 1D26514

## Monday, August 24, 2015

### Converting from Base 13 to Base 10 Problems, 2

Category: Arithmetic

"Published in Newark, California, USA"

Convert 24AC1B313 into Base 10.

Solution:

The given number which is
24AC1B313 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
24AC1B313 into Base 10. How? Let's multiply each digits by the powers of 13 as follows:

Base 6 Digits:       2
4      A     C      1      B      3
Multiply by:
13⁶   13⁵   13⁴   13³   13²   13¹   13

Add all the digits, we have

(2 x 13⁶) + (4 x 13⁵) + (A x 13⁴) + (C x 13³) + (1 x 13²) + (B x 13¹) + (3 x 13) = 9653618 + 1485172 + 285610 + 26364 + 169 + 143 + 3 = 11451079

Therefore,
24AC1B313 = 11451079

## 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