Converting from Base 10 to Base 3 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 685401 into Base 3.
  
Solution:
                                      
The given number which is 685401 is written in Base 10. 685401 can also be written as 685401₁₀. 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 3 number is a number whose digits are 0, 1 and 2. If you see a subscript of 3 at the given number, then that number is written in Base 3. Base 3 number is also called ternary system. 
      
Now, let's convert 685401 into Base 3. How? Let's divide 685401 by 3 as follows:
   
                685401 ÷ 3 = 228467 + R(0)
   
Next, let's divide the quotient, which is 228467, as follows: 
    
                685401 ÷ 3 = 228467 + R(0)
                228467 ÷ 3 =   76155 + R(2)
 
Do the same thing with 76155 until the quotient is 0 as follows:
   
                685401 ÷ 3 = 228467 + R(0)
                228467 ÷ 3 =   76155 + R(2)
                  76155 ÷ 3 =   25385 + R(0)
                  25385 ÷ 3 =     8461 + R(2)
                    8461 ÷ 3 =     2820 + R(1)
                    2820 ÷ 3 =       940 + R(0) 
                      940 ÷ 3 =       313 + R(1) 
                      313 ÷ 3 =       104 + R(1) 
                      104 ÷ 3 =         34 + R(2)  
                        34 ÷ 3 =         11 + R(1)  
                        11 ÷ 3 =           3 + R(2)  
                          3 ÷ 3 =           1 + R(0)  
                          1 ÷ 3 =           0 + R(1)  
                   
The remainders will be the digits of Base 3 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  685401 = 1021211012020₃ 
 

Converting from Base 10 to Base 3 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 951 into Base 3.
  
Solution:
                                      
The given number which is 951 is written in Base 10. 951 can also be written as 951₁₀. 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 3 number is a number whose digits are 0, 1 and 2. If you see a subscript of 3 at the given number, then that number is written in Base 3. Base 3 number is also called ternary system. 
      
Now, let's convert 951 into Base 3. How? Let's divide 951 by 3 as follows:
   
                951 ÷ 3 = 317 + R(0)
   
Next, let's divide the quotient, which is 317, as follows: 
    
                951 ÷ 3 = 317 + R(0)
                317 ÷ 3 = 105 + R(2)
 
Do the same thing with 105 until the quotient is 0 as follows:
   
                951 ÷ 3 = 317 + R(0)
                317 ÷ 3 = 105 + R(2)
                105 ÷ 3 =   35 + R(0)
                  35 ÷ 3 =   11 + R(2)
                  11 ÷ 3 =     3 + R(2)
                    3 ÷ 3 =     1 + R(0) 
                    1 ÷ 3 =     0 + R(1) 
                   
The remainders will be the digits of Base 3 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  951 = 1022020₃ 

Converting from Base 2 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 110111₂ into Base 10.
  
Solution:
                             
The given number which is 110111₂ is written in Base 2. Base 2 number is also called binary system. The digits of Base 2 number are 0, and 1.
   
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 110111₂ into Base 10. How? Let's multiply each digits by the powers of 2 as follows:
         
Base 2 Digits:        1      1      0      1      1      1
Multiply by:            2⁵     2⁴     2³    2²     2¹     2⁰
             
Add all the digits, we have
                 
(1 x 2⁵) + (1 x 2⁴) + (0 x 2³) + (1 x 2²) + (1 x 2¹) + (1 x 2⁰) = 32 + 16 + 0 + 4 + 2 + 1 = 55
             
Therefore, 110111₂ = 55