Numeric conversion check: evaluate the expression 2^(-1) and give its decimal value.

Introduction / Context:Powers of two appear everywhere in digital systems, binary arithmetic, and signal processing. Being fluent with negative exponents is essential when interpreting fractional binary values, fixed-point formats, and resolution steps in analog-to-digital converters.

Given Data / Assumptions:

• The expression is 2^(−1), which denotes a reciprocal power of two.
• We want the decimal (base-10) value.
• No additional scaling or units are involved.

Concept / Approach:A negative exponent indicates a reciprocal: a^(−n) = 1 / (a^n). For base two, common values include 2^(−1) = 1/2, 2^(−2) = 1/4, and 2^(−3) = 1/8. These map directly to fractional steps in binary place values to the right of the binary point.

Step-by-Step Solution:Start with the rule: 2^(−1) = 1 / 2^1.Compute 2^1 = 2.Therefore 2^(−1) = 1 / 2 = 0.5.

Verification / Alternative check:Relate to binary fractions: the first fractional bit (2^(−1)) represents one-half. For example, the binary number 0.1(2) equals 0.5 in decimal, confirming the result.

Why Other Options Are Wrong:

• 0.25 corresponds to 2^(−2).
• 0.1 is 1/10, not a reciprocal power of two.
• 0.05 equals 1/20; again, not a power-of-two fraction.

Common Pitfalls:

• Confusing decimal fractions with binary place values (e.g., interpreting 0.1 as one-tenth regardless of base).
• Misreading the sign of the exponent; negative powers reduce magnitude.

Final Answer:0.5