Octal Number SystemPublished on 24/2/2012 and last updated on 6/9/2018
As its base is 8 = 23, every symbol of this system can be represented by its three bit binary equivalent. As every digit of a number in octal system is represented separately by its three bit binary equivalent the octal system requires one-third of the length as compared to binary numbers. It is basically a positional weighted number system. The digit positions in octal number system has weight as
Octal to Binary ConversionThe conversion is done by converting an individual octal digit to binary. Every digit must be converted to a 3-bit binary number and the resultant will be the binary equivalent of an octal number.
Example Converting (145.56)8 to binary-
This table should be used in order to convert any octal number to binary. From the table, writing binary equivalent of each of the digit we get- which is the binary equivalent of the octal number.
Binary to Octal ConversionThe same table can be used in order to convert a binary number to octal. First, group the binary number into the group of three bits and write the octal equivalent of it.
Example Octal equivalent of (11001111)2 is The groups we got here are- 011,001,111. A zero before the number is added in order to complete the grouping in the form of three binary digits.
Now the octal equivalent of the numbers are- 3, 1, 7. So the octal number we got is (317)8.
Octal to Decimal ConversionThe method of converting an octal number into its decimal equivalent is very simple. Just expand the number in the base of eight with its positional weight and the resultant will be a decimal number.
Example Converting (317)8 to its decimal equivalent. This can be done as follows-
Decimal to Octal ConversionThis can be done by dividing the number by 8 using repeated division method known as double dabble method. The repeated division is done and the remainder is taken. It can be done as follows-
Example Find the octal equivalent of 158. The equivalent number in octal system is (236)8. When there is a number in fraction or after the decimal point, that can be converted as- Say we have to convert 0.40 to octal. So we see that the number is repeated. This will go on and it will be a never ending process so we can approximate the result as- (.3146…)8.
Advantages of Octal Number Systems
- It is of one third length of the binary.
- Easy conversion process from binary to octal and vice-versa.
- Easier to handle input and output in the octal form.