Binary Number System

-

 Binary Number System:

The number system wit base(or radix) two is known  as the binary number system .Only two symbols   are used to represent numbers in this system and these are 0 and 1. These are known as bits. 


Decimal to binary conversion :

Any decimal number can be converted into its equivalent binary number. For integers ,the conversion is obtained by continuous division by 2 and keeping track of the remainder, while for fractional parts, the conversion is affected by continuous multiplication by 2 and keeping track of the integers generated .

Example: Convert (13)10 an equivalent base-2 number 


For Fractional number 

Example: Convert (0.65625)10 to an equivalent base-2 number 

Example: Express the 25.5 decimal numbers in the binary  from :


Binary to Decimal :

Any binary number can be converted into its equivalent decimal number using the weights assigned to each  bit position.

Example: find the decimal equivalent of the binary number (1 1 1 1 1)2



 

Binary  to octal:

Binary numbers can be converted into equivalent octal numbers by making groups of three bits starting from LSB and moving towards MSB for integer part of the number and then replacing each group of three bits by its octal representation.
Example:   Convert (1001110)2  to its octal equivalent 
Solution :                (1001110)2 = (001     001      110)2
                                                   = (1 1 6)8 


Binary to Hexadecimal :

Binary numbers can be converted into the equivalent hexadecimal numbers by making groups of four bits starting from LSB and moving toward MSB from integer part and replacing  each group of four bits by its hexadecimal representation.

Example: Convert the following binary numbers to their equivalent hex numbers.
(a) 10100110101111 

Solution: (10100110101111)2 = 0010    1001    1010    1111   
                                                    2            9            A        F

                  (10100110101111)2 =(29AF)16  


For fractional part:
For the fractional part, the above procedure is repeated starting from the bit next to the binary 
    point and moving towards the right.

(b) (0.00011110101101)2

Solution:  (0.00011110101101)2 = 0.0001    1110     1011    0100
                                                            1            E          B         4

                (0.00011110101101)2 = (0.1EB4)16    




Comments

Post a Comment

Popular posts from this blog

CYBER SECURITY & CRACKING PASSWORDS

-
Image
  CYBER SECURITY We often subscribe to various sites in order to receive exciting offers. Sometimes our email-id comes in the hands of spammers/attackers and here is where you can be in trouble. Since we know, nowadays our email-id is linked to many of our accounts, be it Bank Account, Social Media Accounts or anything else, it’s important to keep it away from attackers .  For those who do not know how phishing works:  Let me put out a scenario in front of you.           Say you have an account in XYZ bank. The spammer comes to know about it.  They create an email-id with the name of the bank which looks genuine.   They use the logo of the XYZ bank and keep it as real as possible.  They send you an email explaining how there is an issue in your bank account and they attach a link, which has to be clicked in order to address the issue.   Now, you click on the link and you are taken to a site, which appea...
Read more

"The Dark Side of Social Media: How It Fuels Digital Addiction and Impacts Mental Health"

-
Image
The Dark Side of Social Media Social media has become an integral part of our lives. We use it to stay connected with friends and family, to learn about the world, and to express ourselves. But what many people don't realize is that social media can also have a dark side. One of the biggest problems with social media is that it can be addictive. The constant stream of notifications and updates can be very stimulating, and it can be hard to pull away. This can lead to problems such as sleep deprivation, anxiety, and depression. The Science of Digital Addiction The science behind digital addiction is largely centered around dopamine and the brain's reward center. Dopamine is a neurotransmitter that plays a crucial role in the brain's reward circuitry, responsible for feelings of pleasure and motivation. When dopamine is released, it reinforces behavior and creates habits. Repeated dopamine release can lead to addiction, as the brain begins to crave the pleasurable feeling ass...
Read more

Online Platforms to Learn Coding

-
Image
  Online Platforms to Learn Coding : 1.Coursera:     Established in 2012, Coursera has developed into a global educational technology enterprise for profit that has delivered more than 1k courses from 100+ institutions.   There are a variety of free introductory programming courses in different areas from universities such as the University of Washington, University of Stanford etc. you can pay for those classes and earn a credential.  2. Udemy:  Udemy is a platform for online education which offers thousands of courses. On the website, there are a lot of paid classes, as well as you can find plenty of free ones too. The courses are not too expensive, special discounts, festival offers, and coupons are available as well.  3.  Code Academy:  Code Academy one of the best in the Business. Many people start their journey from Code Academy and over the years it has gained a lot of reputation in the industry. Using this tool, over 24 m...
Read more