Table of Contents

## List of Numeral System – Unary, Binary, octal and Decimal Number System

Unary numeral system:

This is the simplest numeral system which uses only one symbol, typically a dot or a dash. In this system, 1 is represented by a dot and 2 is represented by a dash. This system is not very commonly used today.

Binary numeral system:

This is the most commonly used numeral system, which uses two symbols, 0 and 1. In this system, 1 is represented by a 1 and 0 is represented by a 0. The binary numeral system is used in digital electronics to represent the numbers of 0 and 1.

Octal numeral system:

This is a numeral system that uses eight symbols, 0 to 7. In this system, 7 is represented by a 7 and 0 is represented by a 0. The octal numeral system is used to represent the numbers from 0 to 7.

Decimal numeral system:

This is the most commonly used numeral system, which uses 10 symbols, 0 to 9. In this system, 9 is represented by a 9 and 0 is represented by a 0. The decimal numeral system is used to represent the numbers from 0 to 9.

## Why Numeration Systems Exist

There are a number of reasons why numeration systems exist. One reason is that it is easier to remember numbers that are represented by symbols than it is to remember the actual sequence of numbers. For example, it is much easier to remember that the number 12 is represented by the symbol “12” than it is to remember that the number 12 is the equivalent of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Another reason why numeration systems exist is because it is often difficult to express certain quantities using just words. For example, it is difficult to say “fifteen thousand two hundred and thirty-seven”. However, it is much easier to say “15,237”.

## History

of the Taj Mahal

The Taj Mahal was built by Mughal Emperor Shah Jahan in memory of his late wife Mumtaz Mahal. Construction of the Taj Mahal began in 1632 and was completed in 1653. The Taj Mahal is made of white marble and is regarded as one of the most beautiful buildings in the world.

## The Bases of Numeration Systems

There are many different numeration systems in use throughout the world. They all have certain characteristics in common, but there are also some important differences.

The most basic characteristic of all numeration systems is that they use symbols to represent numbers. These symbols can be anything from simple tally marks to the numerals we use today.

Another common characteristic is that all numeration systems are base-10. This means that they use 10 symbols to represent the numbers from 0 to 9. The number 10 is represented by the symbol 10 and the number 100 is represented by the symbol 100.

There are a few other base-10 numeration systems in use, such as the Roman numerals. But the most common numeration system in use today is the base-10 system we use in the United States.

## Position in Numeral System

The ordinal number 1st represents the position first in a sequence. It is preceded by 0th and followed by 2nd.

## List of Numeral Systems

There are many different numeral systems in the world. This list includes some of the more common ones.

Base 10

The most common numeral system in the world is base 10. This system uses 10 different symbols to represent numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. In this system, the number 11 is written as 1 + 1 = 2, the number 12 is written as 1 + 2 = 3, and so on.

Base 2

Base 2 is another common numeral system. This system uses just two symbols: 0 and 1. In this system, the number 11 is written as 1 + 1 = 10, the number 12 is written as 1 + 2 = 11, and so on.

Base 16

Base 16 is a numeral system that uses 16 different symbols to represent numbers. In this system, the number 11 is written as 1 + 1 = 10, the number 12 is written as 1 + 2 = 11, and so on. However, the number 10 is written as 1 + 0 = 1, the number 11 is written as 1 + 1 = 2, and so on. This system is often used in computer programming.

## Binary Numeral System

0

1

10

11

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

## The Octal Numeral System

The octal numeral system is the base 8 numeral system, and uses the digits 0 to 7.

In octal, the number “255” is written as “111111”.

The octal numeral system was mainly used in computing in the early days of computing, before the binary numeral system became more popular.

## Decimal Numeral System

The decimal numeral system (also called base 10 or decimal) is the most common system for denoting numbers in the world. It uses 10 symbols, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The number 123, for example, is written as 1, 2, 3, in the decimal numeral system.

The number 123,456,789 is written as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

## Hexadecimal Numeral System

In mathematics, the hexadecimal numeral system is a numeral system with a base of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero through nine, and A–F (or alternatively a–f) to represent values ten through fifteen.

The hexadecimal numeral system was invented by Johannes Kepler in 1618.

A hexadecimal number is composed of sixteen symbols, most often the digits 0–9 and A–F, or alternatively a–f. Hexadecimal numerals are written with the symbols placed left to right in descending order of value, with the most significant digit on the left. For example, the number 1234H (in hexadecimal) is composed of the symbols 1, 2, 3, and 4 in descending order of value, with the most significant digit, 4, on the left.

The hexadecimal number system can be represented as a mathematical equation:

A hexadecimal number can also be represented as a two’s complement binary number. For example, the hexadecimal number 1234H can be represented as the binary number

The hexadecimal number system is used in computer programming, where it is often convenient to use a base 16 numeral system instead of the more common base 10 numeral system. For example, the hexadecimal number 1234H can be represented