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What are Binary Numbers

What are Binary Numbers

Don't look puzzled the next time you see streams of 1s and 0s. If they don't seem to make sense, it's time you update your knowledge of binary numbers.
Manali Oak
Last Updated: Dec 20, 2018
Binary numbers are a part of the numbering system based on 2 in which 0 and 1 are the only digits from which numbers are formed. Unlike the decimal number system in which the base is 10, the base of a binary number is 2. This number system was devised by Pingala, and it serves as the foundation of modern computer technology.
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Before moving ahead, you may like to read all about the history and timeline of computers. After reading this you will realize that binary numbers form the heart of computer systems.
What is Binary Information?
Information that is transmitted across computer networks in the form of binary numbers, as streams of 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 2 raised to the power 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. To find the binary equivalent of a decimal number, we need to keep dividing it by 2 till the quotient is 0 or 1.
Binary number system
The remainders of these divisions are arranged in reverse order, and the string of 1s and 0s thus formed is the binary equivalent of the given decimal.
Consider an example of the decimal number 6. Dividing 6 by 2, the remainder is 0, quotient is 3. Division of 3 by 2 gives 1 as the remainder and 1 as the quotient. Since the quotient is 1, the division stops here. Starting from this 1, and appending to it, the earlier remainders in reverse order, the answer is 110. This is the binary equivalent of 6.
For converting a binary number to decimal, we multiply each digit by a certain power of 2. The power or index is equal to the digit's position in the number (the unit's place digit corresponds to position 0, the ten's place digit is on position 1, and so on).
Here 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
Now that you know the method to convert binary numbers to decimals and vice versa, reading and interpreting them won't be difficult. The only difference between the decimal and binary number systems is that the former operates in base 10, while the latter operates in base 2.