Converting from Base 10 to Base 12 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 74512 into Base 12.
  
Solution:
                                      
The given number which is 74512 is written in Base 10. 74512 can also be written as 74512₁₀. 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 12 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. Since 10 and 11 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 and B = 11. Hence, the digits of Base 12 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B. If you see a subscript of 12 at the given number, then that number is written in Base 12. Base 12 number is also called duodecimal system. 
      
Now, let's convert 74512 into Base 12. How? Let's divide 74512 by 12 as follows:
   
                74512 ÷ 12 = 6209 + R(4)
   
Next, let's divide the quotient, which is 6209, as follows: 
    
                74512 ÷ 12 = 6209 + R(4)
                  6209 ÷ 12 =   517 + R(5)

Do the same thing with 517 until the quotient is 0 as follows:
   
                74512 ÷ 12 = 6209 + R(4)
                  6209 ÷ 12 =   517 + R(5)     

                    517 ÷ 12 =     43 + R(1)
                      43 ÷ 12 =       3 + R(7)
                        3 ÷ 12 =       0 + R(3)
 
The remainders will be the digits of Base 12 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  74512 = 37154₁₂

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