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Binary to Octal Conversion
Binary to Octal Conversion
A binary number can be converted into its equivalent octal number by mapping method. The conversion of a binary number to the octal equivalent is done as per the following steps −
Step 1 − Starting from the binary point, make groups of 3-bits on both sides of the binary point.
Step 2 − Replace each group of 3-bit binary by the equivalent octal digit.
The following table shows the equivalent octal digital for each 3-bit binary group −
| Octal | Binary | ||
|---|---|---|---|
| (2)2 = 4 | (2)1 = 2 | (2)0 = 1 | |
| 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 |
| 2 | 0 | 1 | 0 |
| 3 | 0 | 1 | 1 |
| 4 | 1 | 0 | 0 |
| 5 | 1 | 0 | 1 |
| 6 | 1 | 1 | 0 |
| 7 | 1 | 1 | 1 |
Let us understand the binary to octal conversion with the help of examples.
Example 1
Convert (110011101.110101)2 to its octal equivalent.
Solution
The binary to octal conversion will be performed as follows −
| 3-bit Group | 110 | 011 | 101 | . | 110 | 101 |
| Octal Equivalent | 6 | 3 | 5 | . | 6 | 5 |
Hence, the octal equivalent of given binary number is (635.65)8.
Example 2
Convert (1110111011.11101)2 to octal equivalent.
Solution
The conversion of given binary number to octal number is given below −
| 3-bit Group | 1 | 110 | 111 | 011 | . | 111 | 01 |
| 011 | 110 | 111 | 011 | . | 111 | 010 | |
| Octal Equivalent | 3 | 6 | 7 | 3 | . | 7 | 2 |
Hence, the octal equivalent of (1110111011.11101)2 is (3673.72)8.
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