Reasoning

Number System Maths

A number system is a method of representing numbers on the number line with the help of a set of symbols and rules. These symbols range from 0-9 and are called digits. Let’s learn about the number system in detail, including its types and conversions.

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Number System in Maths

Number System In Maths

A number system in mathematics is a writing system for expressing numbers. It is a mathematical notation for representing numbers of a given set, using consecutive digits or other symbols. It allows us to perform arithmetic operations such as addition, subtraction, multiplication, and division.

Types of Number Systems

1. Decimal Number System (Base-10)

Digits Used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Base: 10
Applications: Universally used in daily life and arithmetic.
Representation: The place value of each digit is a power of 10.

Example: $\times 10^2 + 4 \times 10^1 + 5 \times 10^0$

2. Binary Number System (Base-2)

Digits Used: 0, 1
Base: 2
Applications: Used in computers and digital systems.
Representation: The place value of each digit is a power of 2.

Example: $10112=1×23+0×22+1×21+1×20=11101011_2 = 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 11_{10}$

3. Octal Number System (Base-8)

Digits Used: 0, 1, 2, 3, 4, 5, 6, 7
Base: 8
Applications: Used in computer systems as a shorthand for binary numbers.
Representation: Each digit’s place value is a power of 8.
Example: $3458=3×82+4×81+5×80=22910345_8 = 3 \times 8^2 + 4 \times 8^1 + 5 \times 8^0 = 229_{10}$

4. Hexadecimal Number System (Base-16)

Digits Used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (10), B (11), C (12), D (13), E (14), F (15)
Base: 16
Applications: Widely used in computing to represent binary data compactly.
Representation: Each digit’s place value is a power of 16.
Example: $1A3F=1×162+10×161+3×160=419101A3_F = 1 \times 16^2 + 10 \times 16^1 + 3 \times 16^0 = 419_{10}$

Other Number Systems

Roman Numerals: Ancient numbering system using letters (I, V, X, L, C, D, M).
Base-N Systems: Systems with arbitrary bases (e.g., Base-3, Base-12, Base-20).
Complex Numbers: Combines real and imaginary numbers.
Floating-Point Representation: Used in computers to represent real numbers with fractional parts.

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