Binary-to-decimal conversion practice Convert the 8-bit binary number 10000110₂ to its decimal (base-10) equivalent.

Introduction / Context:Converting between binary and decimal is a core skill in digital electronics and computer architecture. This question reinforces positional weighting of bits in an 8-bit unsigned number.

Given Data / Assumptions:

• Binary input: 10000110₂.
• Unsigned interpretation (no sign bit behavior implied).
• Place values: 2^7 to 2^0 from left to right.

Concept / Approach:Each binary 1 adds its positional weight to the total. For 8 bits, the weights are 128, 64, 32, 16, 8, 4, 2, 1. Sum only those weights where the bit is 1.

Step-by-Step Solution:Write weights under bits: 1 0 0 0 0 1 1 0 → 128, 0, 0, 0, 0, 4, 2, 0.Add active weights: 128 + 4 + 2 = 134.Therefore, 10000110₂ = 134₁₀.

Verification / Alternative check:Convert 134 back to binary: 128 + 4 + 2 → bits at 2^7, 2^2, 2^1 set → 10000110₂, confirming the result.

Why Other Options Are Wrong:144₁₀, 110₁₀, 126₁₀: each includes incorrect weighting or extra/missing powers of two.

Common Pitfalls:Misreading bit positions (especially internal zeros) or forgetting that the leftmost bit is 2^7 in an 8-bit number.

Final Answer:13410