Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Ans. Number systems, within the realm of mathematics, serve as frameworks for representing numbers in diverse formats and are comprehensible to computers. A number, in this context, denotes a mathematical quantity employed for counting, measuring objects, and executing arithmetic operations.
Q2. What is number system in daily life?
Ans. The numerical system assists us in determining the magnitude to which we must confine an object. It provides a broad understanding of the mathematical processes related to specified numbers, facilitating the computation of numbers through mathematical operations.
Q3. What is 10 number system?
Ans. The decimal system, a mathematical positional numeral system, uses 10 as its base and utilizes 10 distinct numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Additionally, it employs a decimal point to signify fractions.
Q4. What is the base 6 number system?
Ans. In summary, heximal, or base six, is a numerical system utilizing the digits 0 through 5 in each place value, as opposed to 0 through 9. Consequently, the representation of the number 6 in decimal becomes 10 in base six. The counting sequence includes 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, and so forth.
Q5. What are the 4 types of number system?
Ans. There are several types of number systems, but the four most commonly used ones are:
1. Decimal Number System (Base-10): This is the most familiar number system, and it uses 10 digits (0-9). Each digit's place value is a power of 10. For example, in the number 325, the "5" is in the ones place, the "2" is in the tens place, and the "3" is in the hundreds place.
2. Binary Number System (Base-2): This system uses only two digits, 0 and 1. It is commonly used in computer science and digital electronics. Each digit's place value is a power of 2. For example, in the binary number 1101, the rightmost "1" is in the ones place, the next "0" is in the twos place, the next "1" is in the fours place, and the leftmost "1" is in the eights place.
3. Octal Number System (Base-8): This system uses eight digits, 0-7. It is less commonly used than binary and hexadecimal but can be found in some computing applications. Each digit's place value is a power of 8.
4. Hexadecimal Number System (Base-16): This system uses sixteen digits, which include the usual 0-9 and the additional A, B, C, D, E, and F to represent the values 10-15. Hexadecimal is often used in computing and programming as a more human-friendly representation of binary-coded values. Each digit's place value is a power of 16.
What is Number System? Types And Questions
The number system, also known as the numeral system, serves as our way of naming or representing numbers.
Praveen Kushwah17 May, 2024
Share
Number System:
The number system, also known as the numeral system, serves as our way of naming or representing numbers. These numbers, fundamental to mathematics, facilitate counting, measuring, and various mathematical calculations. This article breaks down what a number system is, the various types, and how to convert between them with lots of examples.
What is a Number System?
The number system, or numeral system, is how we name or represent numbers. Numbers are those mathematical values we use to count, measure things, and perform various math calculations. In math, we have different systems for expressing numbers, such as the decimal system we commonly use, the binary system, octal system, and the hexadecimal system.
There exist diverse number systems in mathematics, including the commonly used
decimal system, binary system, octal system, and hexadecimal system.
Each system has its unique way of expressing numbers and is essential for different applications.
What is a Number?
A number, in essence, is a mathematical value utilized for counting, measuring, or labeling objects. Numbers are the foundation for performing arithmetic calculations, offering variations such as natural numbers, whole numbers, rational and irrational numbers. Even 0 holds significance as a number, representing a null value.
Numbers come in various forms, with distinctions between even and odd numbers, as well as prime and composite numbers. Even and odd categorizations are based on divisibility by 2, while prime and composite numbers differentiate between those with only two factors and those with more than two factors, respectively.
In the context of a number system, these numbers serve as digits. For instance, binary numbers predominantly use 0 and 1 as digits, while other systems employ digits ranging from 0 to 9. Understanding these number systems is integral to navigating the diverse ways we represent numbers in mathematics.
Types of Number System
There exist various ways to represent numbers. The four most common types are:
Decimal Number System (Base-10):
This system, familiar to us, uses ten digits from 0 to 9. Positions to the left of the decimal point represent units, tens, hundreds, and so on. For instance, the number 1457 is broken down into powers of 10, showcasing its value.
Binary Number System (Base-2):
In binary, there are only two digits: 0 and 1. It's the language of computers, where everything is represented using these two digits. For example, the decimal number 14 can be expressed as 11102 in binary.
Octal Number System (Base-8):
The octal system uses eight digits from 0 to 7. It's often employed in computer applications. Converting an octal number, like 2158, to decimal involves multiplying each digit by powers of 8 and adding them up.
Hexadecimal Number System (Base-16):
Hexadecimal involves base 16, where numbers are represented using both digits and letters (A to F). This system is common in computing. The table illustrates the mapping of numbers in the hexadecimal system.
Understanding these number systems provides a foundation for diverse mathematical applications and computer-related fields.
Number System Conversion
Numbers can wear different outfits like binary, decimal, or hexadecimal. What's cool is that we can easily switch between them! Learn the ropes of these conversions, from decimal to binary and vice versa, or from hexadecimal to binary and back. It's like translating numbers into different languages but in the math world.
Let's Dive into Conversions
Using the conversion procedures we've just learned, let's take a random number, say 349, and see how it looks in different number systems:
In binary, it's 101011101.
In decimal, it's just 349.
Octal fashion gives us 535.
Hexadecimal style spells it out as 15D.
Solving Number System Puzzles
Example 1: Hex to Octal
Let's turn (1056)₁₆ into an octal number. First, convert the hex number to decimal - 4182. Now, by repeatedly dividing by 8, we get (1056)₁₆ = (10126)₈.
Example 2: Binary to Decimal
Take (1001001100)₂. Breaking it down, we get 588 in decimal.
Example 3: Binary to Octal
Convert 10101₂ into octal. Split it as 010 101, and in octal, it reads (25)₈.
Example 4: Hex to Decimal
Turn 2C₁₆ into binary - 00101100. Then, convert to decimal - 44.
Number System Questions
Want a challenge? Try converting (242)₁₀ into hexadecimal, making 0.52 an octal number, or subtracting 110₁₂ from 101₀₂. Test your skills with 5C₆ in decimal or representing binary 1.1 in its decimal form.
1. Convert the decimal number (156)₁₀ into binary.
2. Represent the octal number 765₈ in decimal form.
3. Convert the hexadecimal number 1A3₁₆ into its decimal equivalent.
4. Add the binary numbers 1101₂ and 101₁₀.
5. Change the decimal number (255)₁₀ into its hexadecimal representation.
6. Subtract the octal numbers 527₈ and 314₈.
7. Multiply the binary numbers 101₁₀ and 110₁₀.
8. Convert the hexadecimal number 3F₁₆ into its octal equivalent.
9. Divide the decimal number (648)₁₀ by 9.
10. Represent the fraction 0.75 in binary.
Number System in Computers
Ever wonder how computers understand our words? Well, they speak in numbers! Computers, being numerical wizards, use the binary system but sometimes dabble in octal, decimal, and hexadecimal. It's like a secret code that makes our digital world tick.
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
