- Octal Number System Definition: The octal number system is defined as a base-8 system using digits 0 to 7.
- Octal to Binary Conversion: Convert each octal digit to a three-bit binary number for the binary equivalent.
- Binary to Octal Conversion: Group binary digits in sets of three and convert each to its octal equivalent.
- Octal to Decimal Conversion: Expand the octal number in base-8 with positional weights to find the decimal equivalent.
- Decimal to Octal Conversion: Use repeated division by 8 and record the remainders to convert decimal to octal.
In the early days, the octal number system was mainly used in minicomputers. “OCT” means eight. The octal number system is a base-8 system, meaning it uses 8 symbols: 0, 1, 2, 3, 4, 5, 6, and 7. The smallest two-digit number in this system is (10)8, which equals decimal 8.
In this number system, the number is written as (352)8. You must write the base as 8; otherwise, the number is assumed to be decimal by default. A small error can change the number system base. The main advantage of the octal number system is its easy conversion to binary. Since computers understand only binary number system, converting between binary and octal is straightforward.
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
Number Conversion
Octal to Binary Conversion
The 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 Conversion
The 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 Conversion
The 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 Conversion
This 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.
Disadvantages of Octal Number Systems
Computer does not understand octal number system so there must be a requirement of additional circuitry known as octal to binary converters before it is applied to a digital system or a computer.
