# 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:

 $8^5$ $8^4$ $8^3$ $8^ 2$ $8^1$ $8^ 0$ 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.

Decimal to Octal Conversion

(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 82 + 4 X 81 + 0 X 80 = (224)10

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