# Chapter 1 – Number Systems

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

The method of naming or describing numbers is the number system or the numeral system. In algebra, there are all kinds of number systems, such as binary, decimal, etc. This tutorial covers the numeral system’s entire definitions with their forms, conversions, and queries.

What is the Number System?

As a way of writing to communicate numbers, a number system is specified. This is the mathematical notation for consistently expressing the natural numbers of a given series by using digits or other symbols. It provides each number with a specific representation and represents the figures’ arithmetic and algebraic structure. Arithmetic operations such as addition, subtraction, and division also enable us to work.

In whole numbers, the value of any digit can be calculated by:

• The Digit
• Its place in the number
• The base of the system of numbers

#### Forms of Number System

In mathematics, there are different forms of number systems. The four most prevalent kinds of number system are:

Decimal Machine Number (Base- 10)

System of Binary Numbers (Base- 2)

System of Octal Numbers (Base- 8)

Hexadecimal System of Numbers (Base- 16)

The system with Decimal Number (Base 10 Number System)

Base 10 is a decimal number scheme and it uses ten digits, from 0 to 9. In the decimal number system, units, tens, hundreds, thousands, and so on represent the successive positions to the left of the decimal point. In decimal numbers, this system is expressed.

Each location displays a basic power of the base (10). The decimal number 1457, for example, consists of a digit 7 in the position of the units, 5 in the position of the tens, 4 in the position of the hundreds, and 1 in the position of the thousands, the value of which can be written as

(1 x 10^3) + (4 x 10^2) + (5 x 10^1) + (7 x 10^0)

(1 x 1000) + (4 x 100) + (5 x 10) + (7 x 1)

1000 + 400 + 50 + 7

1457

System of Binary Numbers (Base 2 Number System)

The base 2 number system is often referred to as the binary number system, in which there are only two binary digits, i.e., 0 and 1. Specifically, a radix of 2 is the standard base-2. The numbers described in this system are referred to as binary numbers, a combination of 0 and 1. 110101, for instance, binary integers

System of Octal Number (Base 8 Number System)

The basis is 8 in the octal number system and to represent numbers it uses numbers from 0 to 7. In computer applications, octal numbers are widely used. It is the same as the decimal conversion to convert an octal number to a decimal.

The method with Hexadecimal Number (Base 16 Number System)

Numbers are written or represented in the hexadecimal system using base 16. The numbers are first represented in the hex system, much as in the decimal system, i.e. 0 to 9. Then, using the alphabets of A to F, the numbers are represented.

 Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

#### Computer Numeral System

When we type any letter or word, since computers can only understand rational numbers and irrational numbers, the computer translates them into real numbers. Only a few symbols called digits can be understood by a computer and these symbols describe distinct values depending on the position they hold in the number. The binary number scheme is, in general, used in computers. The octal, decimal, and hexadecimal systems are still often used, however.

#### Conversion of Number System

Numbers can be expressed in all of the divisions of the number system, including binary, decimal, hex, etc. Every number that is expressed in any of the forms of the number system can also easily be translated to another.

#### Conclusion

In this chapter, we learned about the basics of number systems. We learned about the properties Of irrational numbers, types of number systems, and utilizing this base knowledge we can understand the rationalisation laws of radicals. These concepts can be utilized to solve mathematical problems.

#### FAQs

1. What are the 4 types of number systems?

The four most prevalent kinds of number system are:

• Decimal Machine Number (Base- 10)
• System of Binary Numbers (Base- 2)
• System of Octal Numbers (Base-8)
• Hexadecimal System of Numbers (Base- 16)

2. What are the different types of number systems?

The four most prevalent kinds of number system are:

• Decimal Machine Number (Base- 10)
• System of Binary Numbers (Base- 2)
• System of Octal Numbers (Base-8)
• Hexadecimal System of Numbers (Base- 16)

3. What is the highest base number system?

System of Decimal Number [Base-10]

With the least value being 0 and the greatest value being nine. On the left, the digit or column has the greatest value, while on the right, the digit has the least value.

4. What is number system with example?

A system for representing numbers of a certain type (that is, expressing or writing them). Example: There are several systems for the representation of numbers for counting. These include: the usual system of “base ten” or “decimal”:

5. What is the real number system in math?

All rational numbers, such as integer-5 and fraction 4/3, and all irrational numbers, such as √2, are included in the real numbers (1.41421356…, the square root of 2, an irrational algebraic number). Transcendental numbers, such as π, are included within the irrationals.

To learn more about number systems through simple, interactive, and explanatory visualizations, download the MSVgo app.

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electron Beams and Radioactivity
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
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• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
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• Spherical Mirrors
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• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
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• Chemical Reactions And Equations
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• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
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• The d-block and f-block elements
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• The p-Block Elements
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### High School Biology

• Absorption and Movement of Water in Plants
• Adolescent Issues
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• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
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• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
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• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
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• Human Health and Disease
• Human Population
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• Hygiene
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• Integumentary System- Skin
• Kingdom Fungi
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• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Algebra – Quadratic Equations
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Quadrilaterals
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Chemistry in Your Life
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Light, Shadows And Reflections
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Addition
• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time
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