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!