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

● Binary Numbers

• Data and Information

• Number System

• Decimal Number System

• Binary Number System

• Why Binary Numbers are Used

• Binary to Decimal Conversion

• Conversion of Numbers

• Octal Number System

• Hexa-decimal Number System

• Conversion of Binary Numbers to Octal or Hexa-decimal Numbers

• Octal and Hexa-Decimal Numbers

• Signed-magnitude Representation

• Radix Complement

• Diminished Radix Complement

• Arithmetic Operations of Binary Numbers

• Binary Addition

• Binary Subtraction

• Subtraction by 2’s Complement

• Subtraction by 1’s Complement

• Addition and Subtraction of Binary Numbers

• Binary Addition using 1’s Complement

• Binary Addition using 2’s Complement

• Binary Multiplication

• Binary Division

• Addition and Subtraction of Octal Numbers

• Multiplication of Octal Numbers

• Hexadecimal Addition and Subtraction

From Octal Number System to HOME PAGE