Difficulty: Easy
Correct Answer: 0.010
Explanation:
Introduction / Context: Converting fractional values between decimal and binary is a foundational skill in digital electronics and computer architecture. The task is to express 1/4 (which is 0.25 in decimal) exactly as a binary fraction, using correct positional weights to the right of the binary point.Given Data / Assumptions:
Concept / Approach: In binary, each fractional position represents a negative power of 2. The first place after the point is 1/2, the second is 1/4, the third is 1/8, etc. To represent 1/4 exactly, we need a 1 in the 2^-2 place and 0 in all other fractional places.Step-by-Step Solution:
List weights: 2^-1 = 0.5, 2^-2 = 0.25, 2^-3 = 0.125.Match 0.25 to 2^-2.Write binary fraction with only the 2^-2 bit set: 0.01.Option formatting with three fractional digits gives 0.010, which equals 0.01 exactly.Verification / Alternative check:
Convert back: 00.5 + 10.25 + 0*0.125 = 0.25, which is 1/4.Why Other Options Are Wrong:
0.100 equals 0.5 (2^-1), not 0.25.0.110 equals 0.5 + 0.25 = 0.75.0.011 equals 0.25 + 0.125 = 0.375.Common Pitfalls:
Confusing the value of bit positions to the right of the point.Assuming trailing zeros change the value; in binary fractions, 0.01 and 0.010 are equal.Final Answer:
0.010
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