How to do binary conversions. Binary conversion with Examples!

HOW TO DO BINARY CONVERSIONS

To start binary conversions you should know that ,

The table of Decimal Starts from 0 and ends with 9

And Hexa starts with 0 & also ends with 9  but also includes A , B , C , D, E , F .. A for 10 , B for 11, C for 12 , D for 13 , E for 14 and F for 15.. The table of OCTAL starts from 0 and ends with 7 . BINARY has only two numbers or digits 1 & 0.

How to do binary conversions

1. BINARY TO DECIMAL :

  ( 1  0    1   1 )

How to do binary conversions

The number given is a binary number and you have to convert it in DECIMAL . First , you have to know that , To convert a number from binary to decimal you have to apply a formula  2n . 2 is the exponent and n is the power. We will put the number (0,1,2,3,4,...) in place of n and convert it from binary to decimal.

For example :

n=0 (2 power 0 is 1)

n=1 (2 power 1 is 2)

n=2 (2 power 2 is 4 )

n= 3 (2 power 3 is 8)

Now !!

Place these derived numbers with the given decimal number (1   0  1   1)

                       1      0      1      1

                       8      4      2      1

Now the rule says that if the number is ON (having 1 in binary) should be added and if the number having 0 must be cancelled..    

                       1       1        1

                       8  +   2  +    1  =  11 

In this case , we cancelled the number 4 because its binary number is OFF (having a zero) & add 8 , 2 and 1 because their Binary number is ON (having 1)

Our answer is 11 .. Which is a decimal of (1   0   1    1)

BUT ,

if the binary numbers are in points or decimal. How will you convert it into decimal?

Like, 

                 1     0     1  .   1   0    1 

You will solve this by writing in fractions(1/2, 1/4 , 1/8) after decimal & then add with the same method told above:

               1      0      1 .   1     0      1

               4      2      1    1/2  1/4    1/8

               4      +     1      1/2   +  1/8

         Ans:      5   5/8

2. DECIMAL TO BINARY :

1st Method :

Examples:

1. 11 

The conversion is same for decimal to binary . The only difference is we will inverse the process ..

                      8     4    2    1

Write such Binary numbers which make a sum of 11

                      8     4    2    1

                      1     0    1    1 

2. 28

                     16    8      4    2    1

                      1     1      1    0    0

2nd Method : (LCM Method)

Example :

1. 56

                  

                 

In this method , we will take the LCM of the given number but only with 2 . Obviously the remainder is always not zero . The number written with a arrow is the remainder after dividing it from 2 now the answer will be  from tail to head of  the arrow . So , the answer is 111000.

2. 17

Answer :   10001 

3. BINARY TO HEXADECIMAL :

To convert it in HEXADECIMAL , divide the given binary number into two parts and add those whose binary number is ON(equal to 1)

Example #1:

                      

  1        0        1        0    1     0      1     1

                    

   8        4        2        1    8     4      2     1 

         8+2=10                    8+2+1=11

But, in Hexa 10=A and 11=B

Ans : AB

Example #2:

1 0 1 0  0 0 1 1  1 0 0 1  0 1 0 1

8 4 2 1  8 4 2 1  8 4 2 1  8 4 2 1

8+2=10  2+1=3  8+1=9  4+1=5

But ,

10=A in HexaDecimal 

Ans = A395

4.HEXADECIMAL TO BINARY:

Example:

                                 F                5 = ?

                             8  4   2   1    8   4   2   1

  (As F =15... 8+4+2+1=15 & 4 +1)

                       Ans:    1   1    1    1   0   1   0   1 

5. OCTAL TO BINARY:

Example # 1:

*72

Solve:

                     7             2

                 4  2  1         4  2  1

                 1  1  1         0  1  0

Example # 2:

 *28

The number 28 can't convert to BINARY because the range of octal is 0-7 & when we can only use 4 2 1 for conversion . And 4 2 1 gives a sum of 7. So, we can't convert a number which is greater than 7 in OCTAL to BINARY conversion.

Example # 3:

*123

Solve:

              1         2          3

           4 2 1     4 2 1    4 2 1

           0 0 1     0 1 0    0 1 1

6. HEXA TO DECIMAL :

For Hexa  conversion , we will not use 2 power n formula we will use 16n(16 power n)

Then , we will solve with 

n=0(1)

n=1(16)

n=2(256)

n=3(4096)

Example :

*Convert 45 into Decimal ?

                       4             5

                      16            1

Then , multiply both, Like,

4*16=64 & 5*1=5

Add the answers ,

64 + 5 = 69

7.OCTAL TO DECIMAL :

We will use 8 power n formula for Octal conversions

8n  ➝   512   64   8  1 

Example:

                     

                  2      2       3

                 64     8       1

Multiply,

2*64=128 

2*8=16

3*1=3

Then Add the results

128+16+3=147

Answer : 147 

ARITHMETIC IN BINARY :

   0              1             0              1

+ 0          + 0        +   1          +  1

   ㅡ            ㅡ            ㅡ             ㅡ  

   0             1             1              10

Example # 1:

1   0   1

1   1   0

---------

10 1   1

Example #2:

1  0

1  1

-----

10  1

Example #3:

1  1  0

0  1  0

--------

10 0  0

Example #4:

            1     0     1     0    1     1        1

     +     1     0     0     1    0     1        1

            -----------------------------------

            10   1    0       0    0     1       0 

           ------------------------------------

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I tried my level best to guide you in Binary Conversion but if you find any difficulty then you are free to ask in the comment section.

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How to do binary conversions
How to do binary conversions
How to do binary conversions
How to do binary conversions
How to do binary conversions
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