Express the fraction 1/4 as a binary fractional number (base-2 representation).

Introduction:Binary fractions represent values to the right of the binary point using negative powers of 2. Converting a rational fraction such as 1/4 illustrates how place values work in base 2.

Given Data / Assumptions:

• Fraction to convert: 1/4.
• Binary fractional places represent 1/2, 1/4, 1/8, etc.
• No rounding required; 1/4 is exactly representable.

Concept / Approach:The first place to the right of the binary point is 2^-1 = 1/2, the second is 2^-2 = 1/4, the third is 2^-3 = 1/8, and so on. To represent 1/4 exactly, set the 2^-2 place to 1 and the others to 0.

Step-by-Step Solution:

Verification / Alternative check:Compute value of 0.01₂ = 0*(1/2) + 1*(1/4) = 1/4. Exact match, no remainder.

Why Other Options Are Wrong:

• 0.11 = 1/2 + 1/4 = 3/4.
• 0.10 = 1/2.
• 0.00 = 0.

Common Pitfalls:Misreading positions to the right of the point; remember each step halves the weight: 1/2, 1/4, 1/8, etc.

Final Answer:0.01