Our decimal number system uses base or radix “10”. Because we use 10 digits to represent a number. But the binary number system uses base “2” because it uses only two digits zero (0) and one (1) to represent any number. Let’s understand this with an example below:
Decimal number such as 3214 can also be read as three thousand two hundred fourteen and written as
But conventionally we only write coefficients to represent a decimal number and skip the powers of 10. These coefficients are 0,1,2,3,4,5,6,7,8 and 9.
The binary number system has only two possible values 0 and 1 and just like decimal numbers can be written by multiplying 0 and 1 with the powers of 2. But for the sake of simplicity we only right 0 and 1 in a particular sequence. The following table will elaborate more
Major Use of Binary Numerals
The field of digital electronics completely depends on this system. Modern computers are constructed with digital electronic components.Digital computers use binary numbers to operate i.e arithmetic and logical operations. They made possible many scientific, commercial and industrial technology advances which were not possible otherwise.
Using digital computer systems we monitor many business, research and industrial applications in real-time. For example, our space program was not possible without the use of digital computers.
Why was digital computing not possible without binary numbers?
It’s a fact that digital computers can’t work without a binary digit system. They use a sequence of instructions called program which is stored in a memory. These instructions are in the form of electric signals. If decimal numbers are represented by electric signals then each number should have a different voltage or current level.
It means if a computer can handle 1 billion instructions so we have to define 1 billion voltage levels which is impossible and impractical too. Because we need a very large amount of power even to run a pocket PC.
Using a binary number system we can only define two distinct voltage levels high and low (Usually 0V) and define each number with a unique sequence of high and low electrical signals. With this method we can represent any number with two voltage states. The number can be integer, decimal, positive or negative. To do this we need to convert any number, any alphabet, any audio and video data in a sequence of zeros and ones.
How does the digital world Interact with our physical world?
Actually a digital gadget doesn’t understand our language so it uses a converter which takes any information from the physical world and transforms that into a sequence of bits. Another simple name of a sequence is code.
Decimal to Binary Conversion
Decimal to binary conversion is easy. Divide a decimal number by 2 and note down the remainder (either 0 or 1). If the quotient is greater than or equal to 2, then continue dividing a quotient by “2” until you get quotient 1. Lets understand with following example