Table of Contents
Definition and Examples of Octal Number System
An octal number system is a number system that uses base 8. This means that there are 8 possible symbols that can be used to represent numbers: 0, 1, 2, 3, 4, 5, 6, 7. In an octal number system, the number 8 would be represented as 8, the number 9 would be represented as 9, and so on.
An octal number can be written in either base 8 notation or normal notation. In base 8 notation, the number would be written as a string of 8 symbols. For example, the number 8 would be written as 1000. In normal notation, the number would be written as the number 8 followed by the symbol for base 8. For example, the number 8 would be written as 8. In both cases, the number would represent the same number.
Octal numbers are used in some computer systems, such as the original IBM mainframe computers. In these systems, the octal number system was used because it provided a way to represent numbers that was easier to use than the binary number system.
What is a Number System?
A number system is a mathematical system for representing numbers. The most common number system is the base 10 number system, which uses 10 different symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent all the possible combinations of 10 digits (0, 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). The number 26 can be represented as:
26 = 2 x 10 + 6
Types of Number System
There are various number systems in mathematics, but the most commonly used are the natural numbers, the integers, the rational numbers, and the real numbers.
The natural numbers are the counting numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on.
The integers are the whole numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and so on.
The rational numbers are the numbers that can be expressed as a fraction: 1/2, 3/4, 5/8, 7/12, and so on.
The real numbers are all of the numbers that can be expressed on a number line, including the rational numbers and the irrational numbers. The irrational numbers are numbers that cannot be expressed as a fraction, such as pi (3.14159…) and the square root of 2 (1.414213…).
Octal Number System
There are three types of number systems used in mathematics: the decimal number system, the binary number system, and the octal number system.
The decimal number system is the most commonly used number system, and it uses the digits 0 through 9. The binary number system uses the digits 0 and 1, and the octal number system uses the digits 0 through 7.
The octal number system is a base 8 number system, which means that the number 8 is the base of the system. In other words, the number 8 can be represented using the digits 0 through 7. The number 9 can’t be represented in the octal number system, because it requires the digit 8, which is not available in this system.
The octal number system is used mainly in computer programming, where it is often easier to work with octal numbers than with binary numbers.
What is an Octal Number System?
An octal number system is a number system that uses base 8. This means that the number 8 is the base, and the other numbers are formed by multiplying this number by 1, 2, 3, 4, 5, or 6. So, the number 23 in octal would be written as 3*8+5=23.
Conversion From Octal To Binary
Conversion from octal to binary is done by dividing the octal number by 8 and writing down the remainders starting from the right. The number of bits in the binary number is the sum of the remainders.
For example, the octal number 167 is converted to binary as follows:
167 ÷ 8 = 21
21 ÷ 8 = 2
2 ÷ 8 = 0
The binary number for 167 is 1101001.
Conversion From Binary To Octal
To convert a binary number to octal, divide the binary number by 8 and write down the remainders starting from the right.
Example:Convert the binary number 1010 to octal.
1010 / 8 = 1 remainder 2
The octal number for 1010 is 12.
Conversion From Octal To Decimal
To convert octal to decimal, divide the octal number by 8 and take the remainder.
For example, to convert the octal number 5678 to decimal, divide 5678 by 8 and take the remainder:
5678 / 8 = 706.75
706.75 is the decimal equivalent of 5678 in octal.
Conversion From Decimal To Octal
To convert a decimal number to octal, divide the number by 8 and take the remainder. Write the number with the remainder in front of the number, with a dot (.) between the number and the remainder.
For example, to convert the decimal number 5678 to octal:
5678 ÷ 8 = 714
714 R 5
So the octal number for 5678 is 714.5.
Conversion from Octal Number to Hexadecimal Number
The octal number system uses base 8, whereas the hexadecimal number system uses base 16. In order to convert an octal number to a hexadecimal number, simply divide the octal number by 16 and take the remainder. Then, convert the remainder to hexadecimal by using the table below.
Conversion from Hexadecimal Number to Octal Number
To convert a hexadecimal number to an octal number, divide the hexadecimal number by 16 and take the remainder. Then, convert the remainder to octal by using the table below.
Octal Multiplication Table
8 9 10 11 12
1 1 1 1 1
2 2 2 2 2
3 3 3 3 3
4 4 4 4 4
5 5 5 5 5
6 6 6 6 6
7 7 7 7 7
8 8 8 8 8
9 9 9 9 9
10 10 10 10 10
11 11 11 11 11
12 12 12 12 12
Applications of Octal Number System
The octal number system is a base 8 number system that uses the digits 0 through 7. In the octal number system, the number 125 is written as 1125. The number 43 is written as 343.
The octal number system is often used in computer programming, because many computer instructions are represented by octal numbers. For example, the instruction to print the letter “A” on the screen might be written as the octal number 101.
The octal number system can also be used to represent negative numbers. The number -5 would be written as 573.
The octal number system is also useful for representing large numbers. For example, the number 1,728,000 would be written as 17280.
Importance of Octal Number System
The octal number system is one that uses base 8. This means that the number system uses 8 different symbols to represent numbers. The symbols are 0, 1, 2, 3, 4, 5, 6, and 7. In the octal number system, the number 8 is represented as 10. The number 9 is represented as 11. The number 10 is represented as 12. The number 11 is represented as 13. The number 12 is represented as 14. The number 13 is represented as 15. The number 14 is represented as 16. And the number 15 is represented as 17.
