Introduction to Number System | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE) PDF Download

Why so many Number Systems?

Ask most people what the most commonly used number system is, and they would probably reply (after a bit of thought), the decimal system. But actually many number systems, and counting systems are used, without the users thinking much about it. For example clocks and compasses use the ancient Babylonian number system based on 60 rather than the decimal system based on 10. Why? Because 60 is easier to divide into equal segments, it can be evenly divided by 1,2,3,4,5,6,10,12,15, 20 and 30. This is much better for applications such as time, or degrees of angle than a base of 10, which can only be divided into equal parts by 1, 2 and 5.

Many counting systems are ancient in origin and are still in use because they are useful for particular purposes.

Using the decimal system it is easy to count up to ten fingers, using just the fingers on two hands. In northern Britain farmers, for centuries, used an ancient Celtic counting system , based on 20 (also called a score), to count their animals, and its use still persisted even into the second half of the twentieth century.

The binary system, based on 2, is just another special number system, and is used by digital electronic devices because digital circuits work on an electrical ‘on or off’ two state system, a number system based on 2 is therefore much easier for electronic devices to use. However binary is not a natural choice for human counting or calculation.

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FAQs on Introduction to Number System - GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

1. What is the number system?
Ans. The number system is a system of representing numbers using a set of symbols or digits. It includes various bases such as binary (base 2), decimal (base 10), octal (base 8), and hexadecimal (base 16).
2. How does the decimal number system work?
Ans. The decimal number system is a base-10 system, which means it uses ten digits (0-9). Each digit's position in a number represents its value, with the rightmost digit representing ones, the next digit representing tens, the next digit representing hundreds, and so on.
3. What is the binary number system?
Ans. The binary number system is a base-2 system, which means it uses only two digits (0 and 1). In this system, each digit's position represents a power of 2, with the rightmost digit representing 2^0 (1), the next digit representing 2^1 (2), the next digit representing 2^2 (4), and so on.
4. How do you convert a decimal number to a binary number?
Ans. To convert a decimal number to a binary number, you can use the division-by-2 method. Divide the decimal number successively by 2 and note down the remainders from each division. The binary representation is obtained by writing the remainders in reverse order.
5. What is the significance of the hexadecimal number system?
Ans. The hexadecimal number system is a base-16 system that uses digits from 0 to 9 and letters from A to F to represent values from 0 to 15. It is commonly used in computer science and programming as it provides a compact and convenient way to represent large binary numbers. Each hexadecimal digit represents four binary digits, making it easier to work with and understand binary data.
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