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

  • 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
  • Radix Complement
  • Diminished Radix Complement
  • Arithmetic Operations of Binary Numbers





From Octal Number System to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



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.



Share this page: What’s this?

Recent Articles

  1. 4th Grade Mental Math on Roman Numerals | Roman Numerals Quiz

    Feb 23, 24 03:55 PM

    In 4th grade mental math on numbers, students can practice different questions on write the Hindu-Arabic numerals, write the Roman Numerals, comparison of roman numerals, addition of roman numerals.

    Read More

  2. 4th Grade Mental Math on Numbers | Mental Math 4th Grade with Answers

    Feb 23, 24 02:24 PM

    4th Grade Mental Math on Numbers
    In 4th grade mental math on numbers, students can practice different questions on numbers in figures, number name, place value, face value, comparison of number and formation of greatest and smallest…

    Read More

  3. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 23, 24 01:28 PM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More

  4. Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

    Feb 22, 24 04:15 PM

    Roman Numbers Table
    Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…

    Read More

  5. Roman Symbols | What are Roman Numbers? | Roman Numeration System

    Feb 22, 24 02:30 PM

    Roman Numbers
    Do we know from where Roman symbols came? In Rome, people wanted to use their own symbols to express various numbers. These symbols, used by Romans, are known as Roman symbols, Romans used only seven…

    Read More