Converting from Base 11 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 2A193A4₁₁ into Base 10.
  
Solution:
                             
The given number which is 2A193A4₁₁ is written in Base 11. Base 11 number is also called undecimal system. The digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since 10 is not accepted as a digit, then we have to substitute a variable which is A = 10. Hence, the digits of a Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A.
   
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 2A193A4₁₁ into Base 10. How? Let's multiply each digits by the powers of 11 as follows:
         
Base 6 Digits:       2      A      1      9      3      A      4                 
Multiply by:          11⁶   11⁵   11⁴   11³    11²   11¹   11⁰
             
Add all the digits, we have
                 
(2 x 11⁶) + (A x 11⁵) + (1 x 11⁴) + (9 x 11³) + (3 x 11²) + (A x 11¹) + (4 x 11⁰) = 3543122 + 1610510 + 14641 + 11979 + 363 + 110 + 4 = 5180729
             
Therefore, 2A193A4₁₁ = 5180729

Converting from Base 11 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 12A3A₁₁ into Base 10.
  
Solution:
                             
The given number which is 12A3A₁₁ is written in Base 11. Base 11 number is also called undecimal system. The digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since 10 is not accepted as a digit, then we have to substitute a variable which is A = 10. Hence, the digits of a Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A.
   
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 12A3A₁₁ into Base 10. How? Let's multiply each digits by the powers of 11 as follows:
         
Base 6 Digits:        1      2      A      3      A                 
Multiply by:           11⁴   11³    11²   11¹   11⁰
             
Add all the digits, we have
                 
(1 x 11⁴) + (2 x 11³) + (A x 11²) + (3 x 11¹) + (A x 11⁰) = 14641 + 2662 + 1210 + 33 + 10 = 18556
             
Therefore, 12A3A₁₁ = 18556

Converting from Base 10 to Base 11 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 1983425 into Base 11.
  
Solution:
                                      
The given number which is 1983425 is written in Base 10. 1983425 can also be written as 1983425₁₀. 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 11 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since 10 is 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. Hence, the digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A. If you see a subscript of 11 at the given number, then that number is written in Base 11. Base 11 number is also called undecimal system. 
      
Now, let's convert 1983425 into Base 11. How? Let's divide 1983425 by 11 as follows:
   
                1983425 ÷ 11 = 180311 + R(4)
   
Next, let's divide the quotient, which is 180311, as follows: 
    
                1983425 ÷ 11 = 180311 + R(4)
                  180311 ÷ 11 =   16391 + R(10 or A)

Do the same thing with 16391 until the quotient is 0 as follows:
   
                1983425 ÷ 11 = 180311 + R(4)
                  180311 ÷ 11 =   16391 + R(10 or A)

                    16391 ÷ 11 =     1490 + R(1)
                      1490 ÷ 11 =       135 + R(5)
                        135 ÷ 11 =         12 + R(3)
                          12 ÷ 11 =           1 + R(1)
                            1 ÷ 11 =           0 + R(1)
 
The remainders will be the digits of Base 11 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  1983425 = 11351A4₁₁