Number systems: Convert the binary value 1011011₂ to its decimal (base-10) equivalent. Show the positional weights used.

Introduction / Context:Binary-to-decimal conversion reinforces the idea that each bit position represents a power of two. Practicing the expansion method prepares learners for interpreting register contents and memory addresses.

Given Data / Assumptions:

• Binary input: 1011011₂.
• Bit positions from right (LSB) have weights: 2^0, 2^1, 2^2, ...
• Unsigned magnitude, no sign bit.

Concept / Approach:To convert, multiply each bit by its corresponding power-of-two weight and sum the results. Only positions with bit = 1 contribute to the sum.

Step-by-Step Solution:Write weights for 7 bits (MSB→LSB): 64, 32, 16, 8, 4, 2, 1.Match bits 1 0 1 1 0 1 1 → use weights 64, 16, 8, 2, 1.Compute sum: 64 + 16 + 8 + 2 + 1 = 91.Therefore 1011011₂ = 91₁₀.

Verification / Alternative check:Convert back by repeated division by 2 on 91 to reconstruct 1011011₂; the remainders match the bit pattern.

Why Other Options Are Wrong:81₁₀, 100₁₀, 200₁₀: these sums do not equal the expansion of the given bit pattern.None of the above: incorrect because 91₁₀ is correct.

Common Pitfalls:Misaligning bit weights; forgetting to include both the 2 and 1 contributions at the end.

Final Answer:91₁₀