# 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
• Diminished Radix Complement
• Arithmetic Operations of Binary Numbers