4.	Convert 100110112 to decimal. Show every step in your calculation. 

To convert the binary number \( 10011011_2 \) to its decimal (base-10) equivalent, we will use the positional value method. In this method, each digit in the binary number is multiplied by \( 2 \) raised to the power of its position (starting from \( 0 \) at the rightmost digit). Then, we sum the results to get the final decimal value.

Here are the steps:

### Step 1: Write down the binary number and identify the positions
The binary number \( 10011011_2 \) has 8 digits. We will label the positions from right to left starting at 0:
\[
1 \ 0 \ 0 \ 1 \ 1 \ 0 \ 1 \ 1
\]
\[
7 \ 6 \ 5 \ 4 \ 3 \ 2 \ 1 \ 0 \quad \text{(positions)}
\]

### Step 2: Multiply each binary digit by \( 2 \) raised to the power of its position
\[
1 \times 2^7 + 0 \times 2^6 + 0 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0
\]

### Step 3: Calculate each power of 2
\[
= 1 \times 128 + 0 \times 64 + 0 \times 32 + 1 \times 16 + 1 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1
\]

### Step 4: Simplify the expression
\[
= 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1
\]

### Step 5: Sum the results
\[
= 128 + 16 + 8 + 2 + 1 = 155
\]

### Final Answer
The decimal equivalent of \( 10011011_2 \) is \( 155_{10} \).

Would you like more details or have any questions? Here are five related questions to explore:

1. How would you convert the decimal number \( 155 \) back to binary?
2. What is the decimal equivalent of the binary number \( 11111111_2 \)?
3. How do you convert a hexadecimal number to decimal?
4. What is the binary representation of the decimal number \( 200 \)?
5. How would you add two binary numbers, like \( 1001_2 + 1101_2 \)?

**Tip**: Remember, binary uses base-2, where each digit represents a power of 2, starting from the rightmost digit at position 0!

Convert 10011011₂ to decimal. Show every step in your calculation.

Learn how to convert the binary number 10011011₂ to its decimal equivalent with a detailed step-by-step calculation. This guide explains the positional notation method for binary to decimal conversion, perfect for students in Grades 6-8.

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