To convert the binary number \( (1\ 1011)_2 \) to its decimal expansion, let's break it down step by step:

### Step 1: Identify the place values
The binary number \( (1\ 1011)_2 \) is equivalent to:

\[
1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0
\]

### Step 2: Calculate the powers of 2
- \( 2^4 = 16 \)
- \( 2^3 = 8 \)
- \( 2^2 = 4 \)
- \( 2^1 = 2 \)
- \( 2^0 = 1 \)

### Step 3: Multiply each bit by its corresponding power of 2
\[
1 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 = 16 + 8 + 0 + 2 + 1
\]

### Step 4: Add the results
\[
16 + 8 + 2 + 1 = 27
\]

### Conclusion:
The decimal expansion of \( (1\ 1011)_2 \) is \( 27 \).

Would you like more details or have any questions? 

Here are 5 related questions:
1. How do you convert a fractional binary number to decimal?
2. How can you convert decimal numbers back to binary?
3. What is the significance of each bit in a binary number?
4. How do you convert binary numbers larger than 8 bits into decimal?
5. What is the binary equivalent of decimal fractions?

**Tip:** When converting binary to decimal, remember that the rightmost bit represents \( 2^0 \), and each bit to the left increases the power of 2.

Understand how to convert the binary number (1 1011)₂ to its decimal equivalent. This detailed guide explains the binary-to-decimal conversion step-by-step, covering key concepts such as place values and powers of 2. Ideal for students in Grades 6-8.

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