Convert the 8-bit binary number 11001001₂ into its decimal (base 10) value.

Introduction / Context:Binary-to-decimal conversion is fundamental for interpreting register contents, configuration fields, and data payloads. Here we translate an 8-bit binary number into its base-10 value using positional weights, a method that scales to larger bit widths as well.

Given Data / Assumptions:

• Binary input: 11001001₂.
• Unsigned interpretation (no sign or two's-complement concerns).
• Standard positional weights: 2^7 down to 2^0 for 8 bits.

Concept / Approach:Each bit contributes its weight if it is 1. Sum the weights to obtain the decimal value. For an 8-bit number, the weights are 128, 64, 32, 16, 8, 4, 2, 1 from MSB to LSB.

Step-by-Step Solution:

Verification / Alternative check:Break into nibbles: 1100 1001 = C9_hex. Convert C9_hex to decimal: 12*16 + 9 = 192 + 9 = 201. Both methods agree.

Why Other Options Are Wrong:

• 2001: Digit concatenation error, not a base conversion.
• 20: Misses high-order bits 128 and 64.
• 210: Close but incorrect; likely a mis-sum of 128 + 64 + 16 + 2.

Common Pitfalls:Reading bits right-to-left without mapping correct weights, or confusing hex and decimal during intermediate steps. Keep a clear table of weights to avoid mistakes.

Final Answer:201