Numeral system

Сентябрь 12, 2022

Содержание

2. Numeral system (or system of numeration) is a writing system for expressing numbers; that is, a
3. The number the numeral represents is called its value. Ideally, a numeral system will: Represent a
4. The most commonly used system of numerals is the Hindu–Arabic numeral system. Two Indian mathematicians are
5. Decimal numbers (base 10) Represented using 10 numerals: 0, 1, 2, 3, 4, 5, 6, 7,
6. Binary numbers are represented by sequence of bits (smallest unit of information – 0 or 1)
7. Binary numbers (base 2) Represented by 2numerals: 0and 1 Each position represents a power of 2:
8. A text encoding is a system that uses binary numbers (1and 0) torepresent characters Letters, numerals,
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Numeral system
(or system of numeration) is a writing system for

expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner

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The number the numeral represents is called its value.
Ideally,

a numeral system will:
Represent a useful set of numbers (e.g. all integers, or rational numbers)
Give every number represented a unique representation (or at least a standard representation)
Reflect the algebraic and arithmetic structure of the numbers

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The most commonly used system of numerals is the Hindu–Arabic numeral

system. Two Indian mathematicians are credited with developing it. Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero.

Main numeral systems

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Decimal numbers (base 10)
Represented using 10 numerals: 0, 1, 2, 3,

4, 5, 6, 7, 8, 9
Each position represents a power of 10:
401= 4*102+ 0*101 + 1*100 = 400+ 1
130= 1*102 + 3*101+0*100 = 100 + 30
9786= 9*103 + 7*102 + 8*101 + 6*100=
= 9*1000 +7*100 + 8*10 + 6*1

Decimal Numbers

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Binary numbers are represented by sequence of bits (smallest unit of

information – 0 or 1)
Bits are easy to represent in electronics
1 0 0 1 0 0 1 0
1 0 0 1 0 0 1 1
1 1 1 1 1 1 1 1
1 0 1 1 0 0 1 0

Binary Numeral System

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Binary numbers (base 2)
Represented by 2numerals: 0and 1
Each position represents a

power of 2:
101b= 1*22 + 0*21 + 1*20 = 100b + 1b = 4+1= 5
110b = 1*22 + 1*21 + 0*20 = 100b + 10b = 4+2=6
110101b= 1*25 + 1*24 + 0*23 + 1*22 + 0*21+ 1*20=
= 32 + 16 + 4 + 1= = 53

Binary Numbers

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A text encoding is a system that uses binary numbers (1and

0) torepresent characters
Letters, numerals, etc.
In the ASCII encoding each character consists of 8 bits (one byte) of data
ASCII is used in nearly all personal computers
In the Unicode(UTF-16) encoding each character consists of 16 bits (two bytes)
Can represent many alphabets

How ComputersRepresent Text Data?