Binary to Octal Conversion in DLD Digital logic design

Binary to Octal Conversion

• The Binary string is divided into small sub-groups of 3-bits and it is started from the least significant bit.
• After this, needs to identify the each 3 bit binary group.
• At last, each 3-bit binary group is simply replaced by its Octal equivalent number.

Example 1:

Problem:

How to convert this 111010110101110010110  binary number into its octal equivalent?

Solution:

Step 1: Dividing all the bits into groups of 3-bits

• 101   010   110   101   110   110   110

Step 2: 

Replace  each group with a number by its Octal equivalent.

• 101      010      110      101      110      110       110
•   5        2          6           5         6          6           6

Note: Binary strings which can not be divided into equal number of 3- bit groups are supposed to have 0’s  in the left of the bits.

Example 2:

Problem:

How to convert this 1101100010110  binary number into its octal equivalent?

Solution:

Step 1: Dividing all the bits into groups of 3-bits

• 110     110     001     011     0

Step 2: 

Replace  each group with a number by its Octal equivalent.

• 001       101       100        010       110
•   1             5          4             2           6          

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