Number System

Number system is the way to represent anything in the form of numbers and quantities. We use numbers in computers because computers can’t understand human languages like English or Hindi. Instead, they communicate using electricity, which only has two states: on and off. These states are represented as 1 (on) and 0 (off). To process and store data, computers use numbers to represent everything.

To interact with computers, all data, whether it’s a letter, image, or sound, must be converted into numbers. These numbers help the computer understand what we want it to do. And because everything in the computer world is expressed in numbers, learning about number systems is crucial to understanding how computers work.

Types of numbers used in comuters:

• Decimal Number
• Binary Number
• Hexadecimal Number
• Octal Number

Decimal Number

A decimal number uses the base-10 system, which means it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This system is what we use every day for counting and measuring.

So, when we talk about decimal numbers, we’re talking about numbers made up of these ten digits.

It is used in computers because they make it easier for people to read and understand values. While computers primarily use binary (0s and 1s) for processing.

Decimal numbers bridge the gap between how computers work and how people communicate and understand numbers.

Binary Number

The binary number system is the language of computers. Unlike the decimal system, which uses ten digits (0 to 9), the binary system uses only two digits: 0 and 1.

This system is known as Base 2 because it only has these two possible values. In binary, every number is made up of combinations of 0s and 1s. For example, the number 101 in binary doesn’t mean the same thing as 101 in decimal.

In binary, it represents a combination of powers of 2. Just like in decimal where each place represents a power of 10, each place in binary represents a power of 2.

Computers use the binary system because they operate with electrical signals, which are either on (1) or off (0). By using only two states, computers can store and process information reliably.

Although binary is difficult for humans to read, computers can quickly translate it into something we understand, like decimal numbers, so we can interact with them easily.

Hexadecimal Number

The hexadecimal number system, or Base 16, is a system that uses 16 digits instead of the 10 digits used in decimal or the 2 digits used in binary.

The digits in hexadecimal include 0 to 9 (just like decimal), but after 9, it uses the letters A to F to represent the numbers 10 to 15. So, the full set of hexadecimal digits is: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

The hexadecimal number system is used to shorten binary numbers. Binary numbers, which consist only of 0s and 1s, can get very long and difficult for humans to understand.

To make them easier to read, we convert them into hexadecimal, which is much shorter. One hexadecimal digit represents four binary digits, so using hexadecimal helps us work with binary data in a more manageable and readable way.

Octal Number

The octal number system, or Base 8, uses 8 digits: 0 to 7. It’s another way of representing numbers, similar to binary and hexadecimal, but instead of using 2 or 16 digits, it uses 8.

Each digit in an octal number represents a power of 8, just like decimal numbers use powers of 10.

The key reason for using octal in computing is to shorten long binary numbers, much like hexadecimal.Each octal digit can represent 3

binary digits (or bits). So, instead of writing out long binary sequences, you can group them into chunks of three and convert them into octal digits.

Important questions

1. What is a number system?

A number system is a structured way of representing numbers using specific symbols and rules. It defines how numbers are formed and manipulated. For example, the decimal system (base-10) uses ten digits: 0-9.

2. What is the binary number system?

The binary number system is a base-2 system that uses only two digits: 0 and 1. It is the foundation of computer processing, as computers operate using electrical signals that represent these two states.

3. What is the decimal number system?

The decimal number system is the most common system we use in daily life. It is based on ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This system is what we use for counting and measuring.

4. What is hexadecimal?

Hexadecimal is a base-16 number system that uses 16 symbols: 0-9 for values zero to nine and A-F for values ten to fifteen. It provides a more compact way to represent binary data.

5. Why do computers use binary?

Computers use the binary system (base-2) because they operate with electronic circuits that can be either on (1) or off (0). This simple representation matches how computers process information efficiently.

6. What is octal?

Octal is a base-8 number system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Octal is often used in computing as a shorthand method for representing binary data in a more manageable form.

7. How is data stored in computers?

All types of data—like text, images, and videos—are stored as numbers in binary (base-2) form. This allows the computer to manage, retrieve, and process information effectively.

8. What is ASCII?

ASCII (American Standard Code for Information Interchange) is a character encoding standard that assigns numeric values to letters, digits, and symbols. It helps represent text in binary (base-2) form.

9. What are place values in a number system?

Place values indicate the position of a digit in a number, determining its value based on the base of the number system. For example, in the decimal number 345 (base-10), the 3 is in the hundreds place, the 4 is in the tens place, and the 5 is in the ones place.

10. What is the significance of number systems in computing?

Number systems are crucial in computing because they provide the framework for how data is represented, stored, and processed. Computers primarily use the binary system (base-2) to perform calculations and execute commands, while other systems like hexadecimal (base-16) help programmers work with long binary sequences more easily.