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   13⁰
             
Add all the digits, we have
                 
(A x 13⁴) + (1 x 13³) + (2 x 13²) + (B x 13¹) + (C x 13⁰) = 285610 + 2197 + 338 + 143 + 12 = 288300
             
Therefore, A12BC₁₃ = 288300

Converting from Base 10 to Base 13 Problems, 2

Category: Arithmetic

"Published in Newark, California, USA"

Convert 8745699 into Base 13.
  
Solution:
                                      
The given number which is 8745699 is written in Base 10. 8745699 can also be written as 8745699₁₀. 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 13 number is a number whose digits 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 single digit, then we have to use a variable to substitute a two digit number. In this case, let A = 10, B = 11, and C = 12. Hence, the digits of Base 13 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C. If you see a subscript of 13 at the given number, then that number is written in Base 13. Base 13 number is also called tridecimal system. 
      
Now, let's convert 8745699 into Base 13. How? Let's divide 8745699 by 13 as follows:
   
                8745699 ÷ 13 = 672746 + R(1)
   
Next, let's divide the quotient, which is 672746, as follows: 
    
                8745699 ÷ 13 = 672746 + R(1)
                  672746 ÷ 13 =   51749 + R(9)

Do the same thing with 51749 until the quotient is 0 as follows:
   
                8745699 ÷ 13 = 672746 + R(1)
                  672746 ÷ 13 =   51749 + R(9)   

                    51749 ÷ 13 =     3980 + R(9)
                      3980 ÷ 13 =       306 + R(2)
                        306 ÷ 13 =         23 + R(7)
                          23 ÷ 13 =           1 + R(10 or A)
                            1 ÷ 13 =           0 + R(1)
 
The remainders will be the digits of Base 13 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  8745699 = 1A72991₁₃

Converting from Base 10 to Base 13 Problems

Category: Arithmetic

"Published in Newark, California, USA"

Convert 95876 into Base 13.
  
Solution:
                                      
The given number which is 95876 is written in Base 10. 95876 can also be written as 95876₁₀. 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 13 number is a number whose digits 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 single digit, then we have to use a variable to substitute a two digit number. In this case, let A = 10, B = 11, and C = 12. Hence, the digits of Base 13 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C. If you see a subscript of 13 at the given number, then that number is written in Base 13. Base 13 number is also called tridecimal system. 
      
Now, let's convert 95876 into Base 13. How? Let's divide 95876 by 13 as follows:
   
                95876 ÷ 13 = 7375 + R(1)
   
Next, let's divide the quotient, which is 7375, as follows: 
    
                95876 ÷ 13 = 7375 + R(1)
                  7375 ÷ 13 =   567 + R(4)

Do the same thing with 567 until the quotient is 0 as follows:
   
                95876 ÷ 13 = 7375 + R(1)
                  7375 ÷ 13 =   567 + R(4) 

                    567 ÷ 13 =     43 + R(8)
                      43 ÷ 13 =       3 + R(4)
                        3 ÷ 13 =       0 + R(3)
 
The remainders will be the digits of Base 13 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  95876 = 34841₁₃