Converting from Base 10 to Base 5 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 875 into Base 5.
  
Solution:
                                      
The given number which is 875 is written in Base 10. 875 can also be written as 875₁₀. 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 5 number is a number whose digits are 0, 1, 2, 3, and 4. If you see a subscript of 5 at the given number, then that number is written in Base 5. Base 5 number is also called quinary system. 
      
Now, let's convert 875 into Base 5. How? Let's divide 875 by 5 as follows:
   
                875 ÷ 5 = 175 + R(0)
   
Next, let's divide the quotient, which is 175, as follows: 
    
                875 ÷ 5 = 175 + R(0)
                175 ÷ 5 =   35 + R(0)
 
Do the same thing with 35 until the quotient is 0 as follows:
   
                875 ÷ 5 = 175 + R(0)
                175 ÷ 5 =   35 + R(0)
                  35 ÷ 5 =     7 + R(0)
                    7 ÷ 5 =     1 + R(2) 
                    1 ÷ 5 =     0 + R(1) 
                  
The remainders will be the digits of Base 5 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  875 = 12000₅

Converting from Base 4 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 333012₄ into Base 10.
  
Solution:
                             
The given number which is 333012₄ is written in Base 4. Base 4 number is also called quaternary system. The digits of Base 4 number are 0, 1, 2, and 3.
   
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 333012₄ into Base 10. How? Let's multiply each digits by the powers of 4 as follows:
         
Base 4 Digits:        3      3      3      0      1      2          
Multiply by:            4⁵     4⁴     4³    4²     4¹     4⁰    
             
Add all the digits, we have
                 
(3 x 4⁵) + (3 x 4⁴) + (3 x 4³) + (0 x 4²) + (1 x 4¹) + (2 x 4⁰) = 3072 + 768 + 192 + 0 + 4 + 2 = 4038
             
Therefore, 333012₄ = 4038
 

Converting from Base 4 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 213₄ into Base 10.
  
Solution:
                             
The given number which is 213₄ is written in Base 4. Base 4 number is also called quaternary system. The digits of Base 4 number are 0, 1, 2, and 3.
   
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 213₄ into Base 10. How? Let's multiply each digits by the powers of 4 as follows:
         
Base 4 Digits:        2      1      3          
Multiply by:            4²     4¹     4⁰    
             
Add all the digits, we have
                 
(2 x 4²) + (1 x 4¹) + (3 x 4⁰) = 32 + 4 + 3 = 39
             
Therefore, 213₄ = 39