Digital Technique introduction to binary Numbers and ڈیجیٹل تکنیک میں بائنری نمبروں کا تعارف اور بائنری نظام میں گنتی

 

Binary Numbers   

Introduction to binary Numbers.

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Counting in the binary system

بائنری نظام میں گنتی

       

The same type of positional notation is used in the binary number system as in the decimal system.

Although the same positional notation system is used.

 

 

The decimal system uses powers of  10.

The binary system powers of  2.

As was previously explained

 The decimal number of 125.

 Actually means  =  

             1 x 10² + 2 x 101 ⁺ 5 x 10⁰   .

 

In the binary system, 

The same number  = (125) 

is represented as 1111101.

Meaning = 1 x 2⁶ + 1 x 2⁵ + 1 x 2⁴ + 1 x 2³ + 1 x 2² + 0 x 2¹ + 1 x 2⁰.

To express the value of a binary number, therefore, a_{n  - 1} 2^{n -1} + a_{n – 2}  2^{n – 2} + . . . + a₀ is represented as a_{n – 1} a_{n – 1} . . . a₀, where a_i is either 1 or 0 and n is the number of digits to the left of the binary (radix) point.

 

The following examples illustrate the conversion of binary numbers to the decimal system:

  101 =  1 x 2^{3 – 1} + 0 x 2^{3 – 2} + 1 x 2^{3 – 3}

      =  1 x 2² + 0 x 2¹ + 1 x 2⁰

      =  4 + 1 = 5