# Octal Number system and their Conversion

The number with base 8 is called *octal number*. It is represented by Q or O. It was once very popular number system, especially used in the Digital Equipment Corporation PDP/ 8 and other old computers.

It is rarely used today. The octal number system has eight symbols starting from 0 to 7.

*Weight Value:*

32768 | 4096 | 512 | 64 | 8 | 1 |

**Octal to Binary and Binary to Octal Conversion**: The three digit format of binary digits is used for octal to binary conversion or vice versa.

(a) **Octal to Binary**: 3-bits binary numbers are written for each octal digit.

Q. Convert 56 *octal into binary*.

(56)_{8} = (101 110 )_{2}

(b) **Binary to Octal**: The binary numbers are broken into 3-bits sections from LSB to MSB and octal equivalents of each binary section are written.

Q*. Convert 10011 into octal number.*

010011 = 23

(c)** Decimal to Octal**: *Decimal number* is repetitively divided by 8 and remainders are arranged in the form of octal numbers.

*Q. Convert 240 decimal into octal.*

(240)_{10} = (360)_{8}

(d)** Octal to Decimal**: Each octal digit is multiplied by its weighted position. The sum of all products is known as decimal form of octal.

Q. Convert 340 **octal into decimal**.

*Solution,*

(340)_{8} = 3 X 8^{2} + 4 X 8^{1} + 0 X 8^{0} = (224)_{10}

Related posts:

- Binary to Decimal Conversion Conversion binary to decimal and vice versa: We multiply each...
- Binary and Decimal Number System Decimal Number System: The number of base or radix 10...
- Introduction to Number system This is very interesting question, “What is the number?” The...
- Real Number System. Number is one of the basic concept of mathematics. A...
- Type Conversion In C++ Type Conversion In C++ This process of converting one predefined...