Octal Number System

Octal Number System

Octal Number
Number system has a base with 8 is known as octal number. It has eight possible digit 0, 1, 2, 3, 4, 5, 6 & 7.

Octal Number to Decimal conversion:
The format used in octal number is:

                      8³   8²   8¹   8⁰

or in simple form it is : 512,  64,  8,   1

Example:
convert  (2154)₈  into decimal number is
Note : - 2154 has a base 8 because it indicate the number is in octal form.

figure 1

Now multiply the number according to the format of octal number as shown in figure 1. And after multiply simply add the number to get the result.

(2154)₈   = (4 x 1) + (5 x 8) + (1 x 64) + (2 x 512) =  (1132)₁₀

Note:- 1132 has a base 10 because it indicate the number is in decimal form.

so, the conversion of octal number (2154)₈  in decimal form is (1132)_10.

Decimal to octal conversion

Converting a decimal number into an octal number is obtain by the repeated division by 8 method.

 Example 1: Convert the decimal number (266)₁₀ into octal number (?)₈

  Solution:

figure 2

Divide the decimal number by 8 every time as shown in the figure 2 to get the result.

so, the conversion of decimal number  (266)₁₀   into octal number is (412)₈ .

                 (266)₁₀    =   (412)₈

Example 2: Convert the following  decimal number (120)₁₀  into octal number  (?)₈

solution :Apply same method as above.

figure 3

Divide the decimal number by 8 every time as shown in the figure 3 to get the result.

so, the conversion of decimal number  (120)₁₀   into octal number is (170)₈ .

                 (120)₁₀    =   (170)₈

Octal to Binary conversion:
 Octal number is also known as a 3 bit binary number because each digit of an octal number is represented by three binary digits.

figure 4

 For convert an octal number into binary just replace the octal digit by three binary bits.

Example: convert the following octal number  (412)₈  into binary number (?)_2.

solution:              (412)₈  =  (?)₂   

4 = 100

1 = 001

2 = 010

          so, the conversion of octal number into binary number is (412)₈   = (100  001  010)₂ 

 Note: Binary number (100  001  010)₂  has a base 2 because it indicate the number is in binary form.

Example 2: convert the following octal number  (526)₈  into binary number (?)_2.

solution:              (526)₈  =  (?)₂   

5 = 101

2 = 010

6 = 110

          so, the conversion of octal number into binary number is (526)₈   = (101  010  110)₂

Example 3: convert the following octal number  (170)₈  into binary number (?)_2.

solution:              (170)₈  =  (?)₂   

1 = 001

7 = 111

0 = 000

          so, the conversion of octal number into binary number is (170)₈   = (001  111  000)₂

Binary to Octal conversion:
Binary number can be converted to octal number by making groups of three bits starting from LSB and moving towards MSB.

Example 1: convert the binary number ( 100  010   110 ) into octal number (?)₈ 
solution:              100    010   110
                              4         2       6

                      = (426)₈ 
so, the conversion of binary number ( 100  010   110 ) is (426)₈

Note: The number (426)₈  has a base 8 because it represents the number is in octal form.

Example 2: convert the binary number ( 010  110   111 ) into octal number (?)₈ 
solution:              010    110   111
                              2         6       7

                      = (267)₈ 
so, the conversion of binary number ( 010  110   111 ) is (267)₈

Example 3: convert the binary number ( 111  110   000 ) into octal number (?)₈ 
solution:              111    110   000
                              7        6       0

                      = (760)₈ 
so, the conversion of binary number ( 111  110   000 ) is (760)₈