Convert `(37.42)_8` to binary.

Answer

To convert the octal number \( (37.42)_8 \) to binary, we can follow these steps:

### Step 1: Convert each octal digit to its binary equivalent.
Each octal digit can be represented by a 3-bit binary number.

- The octal digit \( 3 \) in binary is \( 011 \).
- The octal digit \( 7 \) in binary is \( 111 \).
- The octal point remains as is.
- The octal digit \( 4 \) in binary is \( 100 \).
- The octal digit \( 2 \) in binary is \( 010 \).

### Step 2: Combine the binary equivalents.
Now we will combine all the binary equivalents we found in Step 1.

- For the whole number part:
- \( 3 \) becomes \( 011 \)
- \( 7 \) becomes \( 111 \)

Combining these gives us:
\[ 011 \, 111 \]

- For the fractional part:
- \( 4 \) becomes \( 100 \)
- \( 2 \) becomes \( 010 \)

Combining these gives us:
\[ 100 \, 010 \]

### Step 3: Write the complete binary number.
Now we can write the complete binary number by combining the whole number part and the fractional part:

\[ (011111.100010)_2 \]

### Final Answer:
Thus, the binary equivalent of \( (37.42)_8 \) is:
\[ (011111.100010)_2 \]

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