what is the number system ?

1. Digital Logic Design

2. Overview
Introduction
Types of Number System
Application
comparison
reference
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3. Introduction
Number systems are systems in mathematics that are used
to express numbers in various forms and are understood
by computers. A number is a mathematical value used for
counting and measuring objects, and for performing
arithmetic calculations. Numbers have various categories
like natural numbers, whole numbers, rational and
irrational numbers, and so on. Similarly, there are various
types of number systems that have different properties,
like the binary number system, the octal number system,
the decimal number system, and the hexadecimal number
system.
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[1]

4. Types of Number System
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5. 1. Decimal
The decimal number system or the base 10 number system uses 10 digits ranging from
0 to 9 to represent any number. The first position from the rightmost part of a decimal
number is known as one's place or unit's place, then the second position is known as
ten's place, and so on. Every decimal number is represented by the power of base 10.
For example, the number 1457 is represented as:
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6. 2. Binary
The binary number system or the base 2 number system uses only two digits i.e. 0 and 1
to represent any number. For example, the decimal number 14 is represented as 1110 in
the binary number system. We need to keep dividing the decimal number by 2 until the
quotient becomes 0 and along with that, we need to remember the remainder. When
the remainders obtained in the division are represented in reverse order, a binary
number is generated.
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7. 3. Octal
The octal number system or the base 8 number system uses 8 digits ranging from 0 to 7
to represent any number. The octal number is very commonly used the computer
systems.
Every octal number is represented by the power of base 8.
For example, the number 215 is represented as:
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8. 4. Hexadecimal
The hexadecimal number system or the base 16 number system uses 16 digits ranging
from 0 to 9 (i.e. 10 digits) and A to F (i.e. 6 digits) to represent any number. Refer to the
chart shown below to know the representation of hexadecimal numbers.
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
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9. We can convert a decimal number into a hexadecimal number. We need to keep
dividing the decimal number by 16 until the remainder becomes 0 and along with that,
we need to remember the remainder. When the remainders obtained in the division are
represented in reverse order, the hexadecimal number is generated.
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10. Number System First Application Second Application
Binary
Storing and
transferring data
within computers and
digital devices.
Digital logic operations like
electronic gates (AND, OR, NOT).
Octal
Representing IP
addresses in
computer networks.
Programming industrial control
systems.
Decimal
Daily financial
calculations like
banking operations
and shopping.
Representing time, date, and
mathematical transactions.
Hexadecimal
Representing colors
in computer graphics
design.
Programming computers and
representing memory addresses.
Application
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11. System Used Digits Highest Value Usage
Decimal 0-9 10^n
Everyday life
and general
computing
Binary 0 and 1 2^n
Computing
and
electronics
Octal 0-7 8^n
Some
programming
and
computing
applications
Hexadecimal 0-9 and A-F 16^n
Programming
and dealing
with
addresses/dat
a
comparison
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12. reference
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https://www.cuemath.com/numbers/number-systems/
https://www.scaler.com/topics/number-system/
https://unacademy.com/content/cat/study-
material/mathematics/number-systems-in-real-life-
situations/
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[2]
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13. Thank
You