How to Convert from Binary to Octal?
Let’s walk through the process of converting binary numbers to octal by using a detailed example to make the concept clear and practical. To begin, we’ll take a binary number and actively break it into groups of three digits, moving outward from the binary point. Next, we’ll replace each group with its corresponding octal value based on a standard reference chart. By following these steps methodically, we’ll transform the binary number into its octal form without losing any accuracy. This hands-on approach not only reinforces understanding but also makes the conversion process much easier to remember and apply in real-world scenarios.
Example: Let’s convert \(\mathsf{1011.00111_{2}}\) to Octal (Base-8).
To convert the binary number \(\mathsf{1011.00111_2}\) into its octal form, begin by identifying the binary point that separates the whole part from the fractional part. From that point, actively form groups of three binary digits as you move outward in both directions—left for the whole number portion and right for the fractional portion. This method works seamlessly because each group of three binary digits directly maps to a single octal digit.
Starting with the whole part, we first take the three digits closest to the binary point: \(\mathsf{011}\). Then, we move left and add two leading zeros to the remaining digit \(\mathsf{1}\), which results in the group \(\mathsf{001}\). For the fractional section, which contains five digits, we begin by forming the group \(\mathsf{001}\). To create the second group, we add one trailing zero to the remaining two digits, forming \(\mathsf{110}\).
After forming all the binary groups, we convert each of them to their octal equivalents using a standard conversion chart. By doing this, we generate the final octal number, ensuring that no precision is lost in the process and that the binary value is faithfully represented.
The octal equivalent for each group of three binary digits is shown first and the chart can be used for future reference.
The actual conversion for this example is shown here
The reverse of this calculation is performed in octal to binary conversion.