Convert `(101100101)_2` to octal.

Answer

To convert the binary number \( (101100101)_2 \) to octal, we can follow these steps:

### Step 1: Group the binary digits into sets of three
Starting from the right, we group the binary digits into sets of three. If the leftmost group has fewer than three digits, we can add leading zeros to make it a complete group.

**Binary Number**: \( 101100101 \)

**Grouping**:
- Starting from the right: \( 101 \) \( 100 \) \( 101 \)

### Step 2: Convert each group to its octal equivalent
Now we convert each group of three binary digits into their corresponding octal values.

- \( 101_2 \) = \( 5_8 \)
- \( 100_2 \) = \( 4_8 \)
- \( 101_2 \) = \( 5_8 \)

### Step 3: Combine the octal digits
Now we combine the octal digits obtained from each group to form the final octal number.

**Octal Number**: \( 545_8 \)

Thus, the binary number \( (101100101)_2 \) converted to octal is \( (545)_8 \).

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