Binary to decimal conversion Convert the binary number 11001001₂ to its decimal (base 10) value.

Introduction / Context:Converting a binary number to decimal reinforces the idea that each bit position represents a power of 2. Understanding positional weights lets you evaluate any base-2 number quickly and accurately.

Given Data / Assumptions:

• Binary number: 11001001₂.
• Bit weights from left (MSB) to right (LSB) for 8 bits: 128, 64, 32, 16, 8, 4, 2, 1.
• Only positions with a 1 contribute to the sum.

Concept / Approach:Write the binary digits aligned with their powers of two and add the weights where the bit is 1. This is the standard positional notation method for base conversion.

Step-by-Step Solution:

Verification / Alternative check:Group into hexadecimal nibbles: 1100 1001₂ = C9₁₆. Convert hex to decimal: C(12)*16 + 9 = 192 + 9 = 201, confirming the result.

Why Other Options Are Wrong:

• 2001: Misplaces the base-10 positional idea; binary 11001001₂ cannot reach thousands.
• 20: Under-counts by ignoring higher-order bits.
• 210: Off by 9 due to arithmetic or bit-weight mistake.

Common Pitfalls:Reading from the wrong end (mixing up MSB and LSB), forgetting a weight, or confusing binary with decimal digit concatenation.

Final Answer:201