Converting from Base 8 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 257413₈ into Base 10.
  
Solution:
                             
The given number which is 257413₈ is written in Base 8. Base 8 number is also called octal system. The digits of Base 8 number are 0, 1, 2, 3, 4, 5, 6, and 7.
   
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 257413₈ into Base 10. How? Let's multiply each digits by the powers of 8 as follows:
         
Base 6 Digits:        2      5      7      4      1      3                 
Multiply by:            8⁵     8⁴     8³    8²     8¹     8⁰   
             
Add all the digits, we have
                 
(2 x 8⁵) + (5 x 8⁴) + (7 x 8³) + (4 x 8²) + (1 x 8¹) + (3 x 8⁰) = 65536 + 20480 + 3584 + 25 + 8 + 3 = 89636
             
Therefore, 257413₈ = 89636

Converting from Base 8 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 472₈ into Base 10.
  
Solution:
                             
The given number which is 472₈ is written in Base 8. Base 8 number is also called octal system. The digits of Base 8 number are 0, 1, 2, 3, 4, 5, 6, and 7.
   
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 472₈ into Base 10. How? Let's multiply each digits by the powers of 8 as follows:
         
Base 6 Digits:        4      7      2                 
Multiply by:            8²     8¹     8⁰   
             
Add all the digits, we have
                 
(4 x 8²) + (7 x 8¹) + (2 x 8⁰) = 256 + 56 + 2 = 314
             
Therefore, 472₈ = 314

Converting from Base 10 to Base 8 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 299012 into Base 8.
  
Solution:
                                      
The given number which is 299012 is written in Base 10. 299012 can also be written as 299012₁₀. 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 8 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, and 7. If you see a subscript of 8 at the given number, then that number is written in Base 8. Base 8 number is also called octal system. 
      
Now, let's convert 299012 into Base 8. How? Let's divide 299012 by 8 as follows:
   
                299012 ÷ 8 = 37376 + R(4)
   
Next, let's divide the quotient, which is 37376, as follows: 
    
                299012 ÷ 8 = 37376 + R(4)
                  37376 ÷ 8 =   4672 + R(0)
 
Do the same thing with 4672 until the quotient is 0 as follows:
   
                299012 ÷ 8 = 37376 + R(4)
                  37376 ÷ 8 =   4672 + R(0)
                    4672 ÷ 8 =     584 + R(0) 
                      584 ÷ 8 =       73 + R(0) 

                        73 ÷ 8 =         9 + R(1)

                          9 ÷ 8 =         1 + R(1)

                          1 ÷ 8 =         0 + R(1)

                  
The remainders will be the digits of Base 8 number. Use the digits of the remainders from bottom to top. Therefore,
   
                  299012 = 1110004₈