To convert the binary number $111001001_2$ to decimal:

Step-by-Step Conversion:

1. Write the binary number and its place values (powers of 2), starting from the rightmost digit: $1 \cdot 2^8 + 1 \cdot 2^7 + 1 \cdot 2^6 + 0 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0$

2. Evaluate the powers of 2: $2^8 = 256, \, 2^7 = 128, \, 2^6 = 64, \, 2^5 = 32, \, 2^4 = 16, \, 2^3 = 8, \, 2^2 = 4, \, 2^1 = 2, \, 2^0 = 1$

3. Multiply each binary digit by its corresponding power of 2: $(1 \cdot 256) + (1 \cdot 128) + (1 \cdot 64) + (0 \cdot 32) + (0 \cdot 16) + (1 \cdot 8) + (0 \cdot 4) + (0 \cdot 2) + (1 \cdot 1)$

4. Simplify: $256 + 128 + 64 + 8 + 1 = 457$

Final Answer:

$111001001_2 = 457_{10}$

Would you like further details or have questions about this process?

Related Questions:

1. How do you convert decimal numbers to binary?
2. What is the binary representation of 457?
3. How can you convert binary numbers to hexadecimal?
4. Why do binary numbers use base 2?
5. What are the practical applications of binary numbers?

Tip:

Always double-check the place