Introduction to the Binary System in Computer Language

 

Good day friends and my good pupils, in this post I'll teach you how to perform number to binary system.This mathematics is one among those mathematics that give some pupils head-heck  and some don't even know what to do when giving this kind of math.

But here I Will show you the most simplest way in solving this.We know that, the only way computer can understand your commands is through binary numbers which are 0's and 1's.

 If you type a word or writing sentences,the only means computer will understand is when the letters or numbers are converted into machine language is 0's and 1's. It's is said that, the only computer language is called binary numbers. Computer don't understand stand English words but in Binary System pattern. If you know you are among those that have this challenge, here you are with a good teacher that will make it easy for you. 

Now, these are examples of binary numbers:

10100₂

110101₂

101110₂. And so on.

And here examples of whole numbers:

28₁₀

12₁₀

54₁₀. And so on

If you are asked to write any binary to number in base ten (10), that means all the binary numbers must be converted to whole numbers. This is how to do it. Every single digits in binary must be added by the same digits, I mean in multiple of 2.

1 0 1₂ = 1     0       1

             4     2       1

1 , 1+1= 2, 2+2= 4. Count it from your right to left.

Finally we have  1 + 4 = 5. The one with 0 means nothing.Let see if 5 is 101 in computer language.

  5

-------- = 2 r 1

  2

   2

---------- = 1 r 0

    2

   

   1

--------- = 0 r 1 

    2

Therefore, 5 is 101₂.

Example 1

Change the following binary numbers to number in base ten.

(a)  1001110₂

(b) 1010001₂

(c) 111001₂

Solution

(a)  1001110₂ =       1           0         0         1         1        1    0          

                             64         32        16        8          4        2     1

                             =   64   +     8   +    4   +    2 

                              =  78₁₀

 

(b) 1010001₂ =  1      0      1     0     0     0      1  

                    =   64   32      16   8     4      2      1

                     =   64   +   16   +    1

                    =  81₁₀

(c)  (c) 111001₂  =      1       1       1      0      0       1

                          =      32     16      8       4      2      1

                         =  32  +   16   +    8   + 1

                         =  57₁₀

That was a great conversion of binary numbers to numbers in base 10. The only scope is that, you place the binary numbers then  start with 1 and add the 1 to another you have 2, then add the 2 till the last number, that is why we call it numbers in base two.

If you have problems based on the above solution, please put them in the comments box.