Converting from Base 10 to Base 2 Problems

Category: Arithmetic

"Published in Newark, California, USA"

Convert 85 into Base 2.

Solution:

The given number which is 85 is written in Base 10. 85 can also be written as 85₁₀. 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 2 number is a number whose digits are 0 and 1. If you see a subscript of 2 at the given number, then that number is written in Base 2. Base 2 number is also called binary system. 

Now, let's convert 85 into Base 2. How? Let's divide 85 by 2 as follows:

                85 ÷ 2 = 42 + R1

Next, let's divide the quotient, which is 42, as follows: 

                85 ÷ 2 = 42 + R(1)
                42 ÷ 2 = 21 + R(0)

Do the same thing with 21 until the quotient is 0 as follows:

                85 ÷ 2 = 42 + R(1)
                42 ÷ 2 = 21 + R(0)
                21 ÷ 2 = 10 + R(1)
                10 ÷ 2 =   5 + R(0)
                  5 ÷ 2 =   2 + R(1)
                  2 ÷ 2 =   1 + R(0) 
                  1 ÷ 2 =   0 + R(1) 

The remainders will be the digits of Base 2 number. Use the digits of the remainders from bottom to top. Therefore,

                  85 = 1010101₂ 

Roman to Hindu Arabic Numeral Problems, 5

Category: Arithmetic

"Published in Newark, California, USA"

Convert MMMDCLXXXMCCLXXV into its equivalent Hindu Arabic numeral.
      
Solution:
  
The given number,  MMMDCLXXXMCCLXXV is a Roman Numeral. In order to convert it into Hindu Arabic Numeral, you must memorize or remember the Roman Numerals Chart.
  
First, let's consider MMM. In Hindu Arabic numeral,  MMM is equivalent to 3,000,000. 3 is 1,000,000s digit.
  
Next, let's consider DC. In Hindu Arabic numeral, DC is equivalent to 600,000. 6 is 100,000s digit.

Next, let's consider LXXX. In Hindu Arabic numeral, LXXX is equivalent to 80,000. 8 is 10,000s digit.

Next, let's consider M. In Hindu Arabic numeral, M is equivalent to 1,000. 1 is 1,000s digit.  

  
Next, let's consider CC. In Hindu Arabic numeral, CC is equivalent to 200. 2 is 100s digit.

Next, let's consider LXX. In Hindu Arabic numeral, LXX is equivalent to 70. 7 is 10s digit.  
   
And lastly, consider V. In Hindu Arabic numeral, V is equivalent to 5. 5 is ones digit.
   
Therefore, MMMDCLXXXMCCLXXV  = 3,681,275.

Roman to Hindu Arabic Numeral Problems, 4

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert CDVMMMXCVIII into its equivalent Hindu Arabic numeral.
      
Solution:
  
The given number,  CDVMMMXCVIII is a Roman Numeral. In order to convert it into Hindu Arabic Numeral, you must memorize or remember the Roman Numerals Chart.
  
First, let's consider CD. In Hindu Arabic numeral,  CD is equivalent to 400,000. 4 is 100,000s digit.
  
Next, let's consider VMMM. In Hindu Arabic numeral, VMMM is equivalent to 8,000. 8 is 1,000s digit.
  
Next, let's consider XC. In Hindu Arabic numeral, XC is equivalent to 90. 9 is 10s digit.
   
And lastly, consider VIII. In Hindu Arabic numeral, VIII is equivalent to 8. 8 is ones digit.
   
Therefore, CDVMMMXCVIII  = 408,098.