Converting from Base 10 to Base 4 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 485 into Base 4.
  
Solution:
                                      
The given number which is 485 is written in Base 10. 485 can also be written as 485₁₀. 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 4 number is a number whose digits are 0, 1, 2, and 3. If you see a subscript of 4 at the given number, then that number is written in Base 4. Base 4 number is also called quaternary system. 
      
Now, let's convert 485 into Base 4. How? Let's divide 485 by 4 as follows:
   
                485 ÷ 4 = 121 + R(1)
   
Next, let's divide the quotient, which is 121, as follows: 
    
                485 ÷ 4 = 121 + R(1)
                121 ÷ 4 =   30 + R(1)
 
Do the same thing with 30 until the quotient is 0 as follows:
   
                485 ÷ 4 = 121 + R(1)
                121 ÷ 4 =   30 + R(1)
                  30 ÷ 4 =     7 + R(2)
                    7 ÷ 4 =     1 + R(3) 
                    1 ÷ 4 =     0 + R(1) 
                   
The remainders will be the digits of Base 4 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  485 = 13211₄

Converting from Base 3 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 101221₃ into Base 10.
  
Solution:
                             
The given number which is 101221₃ is written in Base 3. Base 3 number is also called ternary system. The digits of Base 3 number are 0, 1, and 2.
   
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 101221₃ into Base 10. How? Let's multiply each digits by the powers of 3 as follows:
         
Base 3 Digits:        1      0      1      2      2      1    
Multiply by:            3⁵     3⁴     3³    3²     3¹     3⁰   
             
Add all the digits, we have
                 
(1 x 3⁵) + (0 x 3⁴) + (1 x 3³) + (2 x 3²) + (2 x 3¹) + (1 x 3⁰) = 243 + 0 + 27 + 18 + 6 + 1 = 295
             
Therefore, 101221₃ = 295

Converting from Base 3 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 121₃ into Base 10.
  
Solution:
                             
The given number which is 121₃ is written in Base 3. Base 3 number is also called ternary system. The digits of Base 3 number are 0, 1, and 2.
   
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 121₃ into Base 10. How? Let's multiply each digits by the powers of 3 as follows:
         
Base 3 Digits:        1      2      1    
Multiply by:            3²     3¹     3⁰   
             
Add all the digits, we have
                 
(1 x 3²) + (2 x 3¹) + (1 x 3⁰) = 9 + 6 + 1 = 16
             
Therefore, 121₃ = 16