Binary to Decimal Number system | Decimal to Binary System | Radix

 We use decimal system of numeration in our daily lives but computers don't. Computers use binary mathematical notation which has digits 1 and 0. The explanation why it is implemented and widely used because its really easy to store 2 states of knowledge instead of 10.


  Binary mathematical notation is employed to store information in computer. Binary numbers are more accurate and readable mathematical notation. Performing calculations is perfectly easy with these numbers. Binary numbers system has 2 logic systems. They are positive logic system and negative logic system.


1)Positive logic system: 1 is represented as true or with +5volts.0 is represented as false or with volts.

 

2)Negative logic system: 1 is represented as false or with 0volts.0 is represented as true or with +5 volts.


 Many number systems were developed to process information in computer but it often added complexity in computer functioning. a number of the opposite number systems are octal and hexadecimal numbers system. 

Hexadecimal system of numeration is employed in html and CSS for giving the knowledge a couple of certain color. Every mathematical notation incorporates a Radix. lets examine what radix means.


Radix: Radix is the number of digits present in a very number representation system. Radix plays an important role in understanding about binary weightage which we are going to discuss further.

For example: Radix of decimal number system is 10,because the number system has 10 digits in it 0,1,2,3,4,5,6,7,8,9.
So the radix of binary numeration system is 2 as it has 1and 0 as it's digits.


Binary weightage: in decimal number system, the radix is 10 and when we move from unit's place to the left at the  ten's place we are increasing the exponential power of 10.

In binary number system we increase the exponential power of 2 when to left. So the binary weightage helps us to calculate the decimal equivalent. It also helps in conversion of binary number to decimal number.

Converting binary number to decimal:


Examples:

 i) Convert (1001) into decimal
           Step 1: Write the given binary number.
          =   1  0  0  1
           Step 2:Write the binary weightage below each number
          =  1  0   0  1
          =  8+4+2+1
           Step 3:Cancel the weightage, which is placed below 0 because any number multiplied by zero is zero.
          = 1  0  0  1
          = 8+4+2+1
           Step 4:Add the remaining numbers.
          = 8+1
          Therefore, (1001) = (9)

ii) Covert (110011) into decimal
  = 1     1   0   0  1  1
  =32+16+8+4+2+1
  =32+16+8+4+2+1
  =(51)
  Therefore,(110011) = (51)

iii) Convert (10101.101) into decimal
 = 1   0   1  0  1  .    1       0      1
 =16+8+4+2+1  .+0.5+0.25+0.125
 =(21.625)
   Therefore,(10101.101) = (21.625)


Decimal to binary conversion


1) To Covert decimal number into binary number we will be using the double dabble method. Before that lets us know what MSB and LSB stands for.

MSB: It is know as the most significant bit of a number. It represents the first digit from left. Its the most weightage in an exceedingly binary number.

LSB: It is know as the least significant bit of a number. It represents the last digit from left. It has the minimum weightage in a binary number.

To convert a decimal number into binary number divide it with 2 till you get 1 because the dividend.
  

Fractional decimal number to binary conversion

To convert fractional decimal number to binary we multiply each bit by 2.Then we take the amount at the proper of percentage point.

(Note: just in case of strange fractional number find the binary number up to 4 to 5 digits to use approximation.)

Frequently asked Questions.

1) Who named numbers ?
=>The Egyptians .

2) What's number base ?
=> Number base is a collection of digits used to represent numbers.


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