CONVERSION BEETWEEN OCTAL AND BINARY BY TWO METHODS

Conversion Octal To Binary:

We can Convert Octal number into binary no by two methods:-

1. Convert Octal to Decimal and again Convert Decimal into Binary.

Ex-  (256)8=(?)2

Sol.  Convert it in Decimal

         (256)8

        =2x8² + 5x8¹ + 6 x 8⁰

        =2x64+5x8+6x1

        =128+40+6

        = (174)₁₀

          Now Convert it into Binary,

2	174	R
2	87	0
2	43	1
2	21	1
2	10	1
2	5	0
2	2	1
	1	0

(174)10=(10101110)₂

2. Convert to Octal to Binary with the help of list.

Determine the value of each digit according to the geven list:

0=000

1=001

2=010

3=011

4=100

5=101

6=110

7=111

Steps:-

• Write  the value of each Digit according the list.
• The formed number is equivalent to Binary.

Ex-  (256)8=(?)2

Sol.  Convert it in Binary with the help of list.

         (256)8=(010101110)2

                      =(10101110)2

Conversion Binary To Octal:

We can Convert binary number into Octal no by two methods:-

1. Convert Binary to Decimal and again Convert Decimal into Octal.

Ex-  

(10101110)₂=

= 1x2⁷ + 0x2⁶ +1x2⁵ +0x2⁴ + 1x2³ + 1x2² + 1x2¹ + 0x2⁰

=1x128+0x64 + 1x32 + 0x16 + 1x8 + 1x4 + 1x2 + 0x1

= 128+32+8+4+2

= (174)₁₀

          Now Convert it into Octal,

8	174	R
8	21	6
	2	5

(174)10=(256)₈

2. Convert to Binary to Octal with the help of list.

Determine the value of each digit according to the geven list:

0=000

1=001

2=010

3=011

4=100

5=101

6=110

7=111

Steps:-

• Write  the value of each Digit according the list.
• The formed number is equivalent to Binary.

Ex-  (10101110)₂=(?)₈

Sol.  Convert it in Octal with the help of list.

         (10101110)2

        =10  101  110

        =010  101  110 (Add '0' to make three digit)

        = (256)₈