How to convert from binary to base 8.

To convert from binary to base 8, you can group the binary digits into sets of three starting from the rightmost digit. If there are not enough digits to form a group of three, add leading zeros to make a complete group.

Then, convert each group of three binary digits into its equivalent octal digit using the following conversion table:

Binary: 000 001 010 011 100 101 110 111
Octal: 0 1 2 3 4 5 6 7

For example, let's convert the binary number 1101011 to base 8:

1. Group the binary digits into sets of three: 001 101 011
2. Convert each group to its octal equivalent: 1 5 3
3. Combine the octal digits to get the final result: 153

Therefore, the binary number 1101011 is equivalent to the octal number 153.

Step 1: Group Binary Digits into Triads

- Start from right to left and group the binary digits into triads (groups of three).
- Pad with leading 0s if necessary to complete the triads.

Step 2: Convert Each Triad to Base 8

- Use the following table to convert each triad to its corresponding base 8 digit:

| Binary Triad | Base 8 Digit |
|---|---|
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |

Step 3: Write the Base 8 Digits in Order

- Concatenate the converted base 8 digits to form the base 8 number. The order should be from left to right, starting with the most significant digit.

Example:

Convert binary 10010110 to base 8.

Step 1: Group into triads: 010 010 110

Step 2: Convert triads to base 8: 2 2 6

Step 3: Write the base 8 digits in order: 226

Therefore, 10010110 in binary is equivalent to 226 in base 8.