This article explains the Octal Number System. It also provides a method to convert decimal numbers to octal and octal numbers to decimal, along with an example.
What is Octal Number System?
The Octal Number System uses only eight digits: 0, 1, 2, 3, 4, 5, 6, and 7, with a base or radix of 8. The digits from 0 to 7 in the octal system have the same meaning as in the decimal system. However, decimal numbers from 8 to 15 are represented as 10, 11, 12, 13, 14, 15, 16, and 17, respectively, in the octal system.
In the Octal Number System, each significant position has a positional weight. The least significant position has a weight of 8^0, which is 1. The higher significant positions are given weights in ascending powers of 8, i.e., 8^1, 8^2, 8^3, and so on.
Decimal to Octal Conversion:
To convert a decimal number into an octal, we divide the decimal number by 8 progressively until we get a quotient of 0. The remainders obtained in each step of division, when read in reverse order, give the equivalent octal number. This conversion method is similar to the double-dabble method.
Let’s see an example of converting the decimal number (444.456) into its equivalent octal number. First, we separate the integer and fraction parts of the decimal number.
To convert the integer part of the decimal into an octal, we repeatedly divide the integer by 8 until we get a quotient of 0. We record the remainder in each step of division and arrange them in reverse order. For example:
Division Generated Remainder
Reading the remainders from bottom to top, the decimal number (444) is equivalent to octal (674).
To convert the fraction part of the decimal into octal, we continuously multiply the fraction by 8. We record the carry at the integer position in each multiplication. The process of multiplication is terminated when we obtain the desired number of significant digits. The carry, when read in forward order, gives the octal form of the fractional decimal. For example:
Multiplication Generated Carry at Integer Position
This is shown below.
|Multiplication||Generated Carry at Integer Position|
|8×0.456 = 3.648||3|
|8×0.648 = 5.184||5|
|8×0.184 = 1.472||1|
|8×0.472 = 3.776||3|
|8×0.776 = 6.208||6|
Reading the carry from top to bottom gives the equivalent octal number. Therefore, the decimal (0.456) is equivalent to an octal (.35136).
Thus, the decimal number (444.456) is equivalent to an octal (674.35136).
Octal to Decimal Conversion:
In octal, each significant position has a positional weight. The least significant position has a weight of 8^0, which is 1. The higher significant positions are given weights in ascending powers of 8, i.e., 8^1, 8^2, 8^3, and so on. The digits after the octal point have weights of 8^-1, 8^-2, 8^-3, and so on. Octal to Decimal Conversion Example
What is the difference between octal and decimal?
The number system represents numbers by their bases. There are four bases for numbers: binary, octal, decimal, and hexadecimal. If the base is 2, it is binary; if it is 8, it is octal; if it is 10, it is decimal, and if it is 16, it is hexadecimal.
Why is octal used?
The main advantage of using Octal numbers is that they have fewer digits compared to decimal and Hexadecimal numbers. This means there are fewer calculations and fewer chances of making mistakes. Octal numbers also use only 3 bits to represent any digit in binary, making it easy to convert between octal and binary, back and forth.
Where is octal used?
The Octal Number system is used a lot in computers and digital systems. Computers use 16-bit, 32-bit, or 64-bit words, which are then divided into 8-bit words. Octal numbers are also used in aviation as a code.
What is the difference between binary and octal?
Binary and Octal number systems are different from the decimal number system in how we write numbers. In the binary system, we only use 0 and 1 digits, while in the octal system, we use digits from 0 to 7 to write numbers.
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