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 Â binary number into its octal equivalent?

Solution:

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

• 101 Â  010 Â  110 Â  101 Â  110 Â  110 Â  110

Step 2:Â

Replace Â each group with a number by its Octal equivalent.

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

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

Example 2:

Problem:

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

Solution:

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

• 110 Â  Â  110 Â  Â  001 Â  Â  011 Â  Â  0

Step 2:Â

Replace Â each group with a number by its Octal equivalent.

• 001 Â  Â  Â  101 Â  Â  Â  100 Â  Â  Â  Â 010 Â  Â  Â  110
• Â  1 Â  Â  Â  Â  Â  Â  5 Â  Â  Â  Â  Â 4 Â  Â  Â  Â  Â  Â  2 Â  Â  Â  Â  Â  6 Â  Â  Â  Â  Â
Prof.Fazal Rehman Shamil (Available for Professional Discussions)
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