# Octal Number System

Octal number system has a base or radix 8. Eight different symbols, namely 0, 1, 2, 3, 4, 5, 6, 7 are used to represent octal numbers. Conversion of octal numbers to their decimal equivalents can be accomplished by using the same rule which was followed to convert binary numbers to decimal numbers, except that we now have a radix 8 instead of 2. Thus the octal number 273 has the decimal equivalent.

2738

= 2 × 82 + 7 × 81 + 3 × 80

= 128 + 56 + 3

= 18710

Conversion of decimal I integers to octal can be performed by successively dividing number by 8 and using each remainder as a digit of the desired octal number. We note that the first remainder is the least significant digit and the last one is the most significant digit. In the case of decimal fractions, we use the same method which was used in converting decimal fractions to binary fractions.

Few examples on octal number system are explained with this method:

Convert the decimal numbers to their octal equivalents:

(a) 2980

Solution:

2980

Hence 298010 = 56448

(b) 0.685

Solution:
0.685

### Decimal Numbers to Binary Number Conversion Table

Multiplication Integer Fraction
0.685 × 8 = 5.480 5 .48
0.48 × 8 = 3.84 3 .84
.84 × 8 = 6.72 6 .72
.72 × 8 = 5.76 5 .76

Therefore, 0.68510 = (0.5365…)8

• Why Binary Numbers are Used
• Binary to Decimal Conversion
• Conversion of Numbers
• Hexa-decimal Number System
• Conversion of Binary Numbers to Octal or Hexa-decimal Numbers
• Octal and Hexa-Decimal Numbers
• Signed-magnitude Representation
• Arithmetic Operations of Binary Numbers

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Intersecting Lines | What Are Intersecting Lines? | Definition

Jun 14, 24 11:00 AM

Two lines that cross each other at a particular point are called intersecting lines. The point where two lines cross is called the point of intersection. In the given figure AB and CD intersect each o…

2. ### Line-Segment, Ray and Line | Definition of in Line-segment | Symbol

Jun 14, 24 10:41 AM

Definition of in Line-segment, ray and line geometry: A line segment is a fixed part of a line. It has two end points. It is named by the end points. In the figure given below end points are A and B…

3. ### Definition of Points, Lines and Shapes in Geometry | Types & Examples

Jun 14, 24 09:45 AM

Definition of points, lines and shapes in geometry: Point: A point is the fundamental element of geometry. If we put the tip of a pencil on a paper and press it lightly,

4. ### Subtracting Integers | Subtraction of Integers |Fundamental Operations

Jun 13, 24 04:32 PM

Subtracting integers is the second operations on integers, among the four fundamental operations on integers. Change the sign of the integer to be subtracted and then add.