# Prepare GK

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### Binary System

The basic unit for computer data storage is called a bit short for the word binary digit.

These bits are numbers 1 and 0, which use the binary language to communicate with computers. So, all the files stored in our computers are translated into words, pictures, audio by the software. The system of 1 and 0 is called 'binary number system', because it has only these two numbers. Binary numbers make up the numbering system that is based on 2 in which 0 and 1 are the only available digits to form numbers. Unlike the decimal number system in which the base is 10, the base of every binary number is 2.

The information that is transmitted across computer networks in the form of binary numbers, as streams as 0s and 1s, is known as binary information.

Each digit of a binary number represents an increasing power of 2. The right-most digit, which is conventionally known as the unit's place digit in context of decimal numbers, represents 2 to the power 0. The next digit represents 2 to the power 1, the next is base 2 raised to the index 2, then 2 raised to the power 3 and so on.

In the binary numeral system, the numbers 0 and 1 are represented as 0 and 1 respectively. They remain unchanged. The number 2 is represented as 10, 3 as 11, 4 as 100, 5 as 101 and so on.

Following is an example of the binary representation of 5.
101 = 1*22 + 0*21 + 1*20
= (1*4) + (0*2) + (1*1)
= (4) + (0) + (1) = 5

Rules on How To Convert Decimal To Binary

The rule is to divide a given decimal number by 2 and make a note of the remainder. Continue dividing, until you cannot divide by 2 anymore. When you note down the remainders starting from the bottom, you get the binary number. The rule is simple and you will get a hold of it by the help of the following examples.

Decimal to Binary Conversion of Number 10

10 ÷ 2 = 5, remainder is 0
5 ÷ 2 = 2, remainder is 1
2 ÷ 2 = 1, remainder is 0
1 ÷ 2 = 0, remainder is 1

Now the division stops here, as there is nothing to divide further by 2. So, as I said, starting from the bottom, write down the remainders and work your way up the list. In this case, it will be 1010 (starting from the bottom remainder). Thus, 1010 = 10102.

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