OCTAL NUMBER SYSTEM
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010.
Octal Number system is based on 8. 8 numerals from 0 to 7 are used in this system.
A number system which has its base as ‘eight’ is called an Octal number system. It uses numbers from 0 to 7. Let us take an example, to understand the concept. As we said, any number with base 8 is an octal number like 248, 1098, 558, etc.
Like Octal number is represented with base 8, in the same way, a binary number is represented with base 2, decimal number with base 10 and the hexadecimal number is represented with base 16.
Examples for these number systems are:
222 is a binary number
10010 is a decimal number
4016 is a hexadecimal number
If we solve an octal number, each place is a power of eight.
1248= 1 × 82 + 2 × 81 + 4 × 80
Characteristics of octal number system are as follows:
- Uses eight digits, 0, 1, 2, 3, 4, 5, 6, 7.
- Also called base 8 number system.
- Each position in an octal number represents a 0 power of the base.
- Last position in an octal number represents a x power of the base.
Representation of octal number system:
The equivalent binary number of Octal number are as given below −
Octal number system is similar to Hexadecimal number system. Octal number system provides convenient way of converting large binary numbers into more compact and smaller groups, however this octal number system is less popular.
. Since base value of Octal number system is 8, so there maximum value of digit is 7 and it can not be more than 7. In this number system, the successive positions to the left of the octal point having weights of 80, 81, 82, 83 and so on.
Similarly, the successive positions to the right of the octal point having weights of 8-1, 8-2, 8-3and so on. This is called base power of 8. The decimal value of any octal number can be determined using sum of product of each digit with its positional value.
Applications of Octal Number System
The octal numbers are not as common as they used to be. However, Octal is used when the number of bits in one word is a multiple of 3. It is also used as a shorthand for representing file permissions on UNIX systems and representation of UTF8 numbers, etc
Advantages and Disadvantages of the Octal Number System:
Advantages:
The main advantage of using Octal numbers is that it uses less digits than decimal and Hexadecimal number system. So, it has fewer computations and less computational errors. It uses only 3 bits to represent any digit in binary and easy to convert from octal to binary and vice-versa. It is easier to handle input and output in the octal form.
Disadvantages:
The major disadvantage of Octal number system is that computer does not understand octal number system directly, so we need octal to binary converter.
7’s and 8’s Complement of Octal (Base-8) Number
Simply, 7’s complement of a octal number is the subtraction of it’s each digits from 7. For example, 7’s complement of octal number 127 is 777 - 127 = 650.
8’s complement of octal number is 7’s complement of given number plus 1 to the least significant bit (LSB). For example 8’s complement of octal number 320 is (777 - 320) + 1 = 457 + 1 = 460. Please note that maximum digit of octal number system is 7, so addition of 7+1 will be 0 with carry 1.
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