To convert the binary number 11011 into its decimal (base 10) equivalent, which is 55, you can follow these steps:

Step 1: Understand the positional values

Each digit in a binary number represents a power of 2, starting from the right (with the power of 0). For 11011, the positional values are as follows:

• $1 \times 2^4$
• $1 \times 2^3$
• $0 \times 2^2$
• $1 \times 2^1$
• $1 \times 2^0$

Step 2: Apply the powers of 2

Calculate the powers of 2 for each position:

• $1 \times 2^4 = 1 \times 16 = 16$
• $1 \times 2^3 = 1 \times 8 = 8$
• $0 \times 2^2 = 0 \times 4 = 0$
• $1 \times 2^1 = 1 \times 2 = 2$
• $1 \times 2^0 = 1 \times 1 = 1$

Step 3: Add the results

Now, add the values from all positions:

$16 + 8 + 0 + 2 + 1 = 27$

So, the binary number 11011 equals 27 in decimal.

However, if you're trying to convert the binary number 110111 to decimal (this seems closer to 55), the process is:

Example: Convert 110111 to decimal

1. Identify positional values:

   • $1 \times 2^5 = 32$
   • $1 \times 2^4 = 16$
   • $0 \times 2^3 = 0$
   • $1 \times 2^2 = 4$
   • $1 \times 2^1 = 2$
   • $1 \times 2^0 = 1$

2. Sum these: $32 + 16 + 0 + 4 + 2 + 1 = 55$

Thus, the binary number 110111 equals 55 in decimal.

Would you like further details or have any questions?

5 Related Questions:

1. How do you convert decimal numbers to binary?
2. What are binary numbers used for in computing?
3. Can you explain how to convert larger binary numbers to decimal?
4. How does the binary system relate to hexadecimal numbers?
5. What are positional number systems, and how do they work?

Tip:

When converting binary to decimal, always start by writing the powers of 2 from right to left for each digit!