The integer part 111₂ equals 1×4 + 1×2 + 1×1 = 7. The fractional part .001₂ equals 0×1/2 + 0×1/4 + 1×1/8 = 1/8 = 0.125. Adding these components yields 7 + 0.125 = 7.125. Therefore, the decimal equivalent of 111.001₂ is 7.125.
Option A:
Option A correctly computes both the integer and fractional contributions and combines them. It uses the appropriate negative powers of 2 for the bits after the point, giving a precise decimal value of 7.125.
Option B:
Option B, 7.25, would require the fractional part to be .01₂ (1/4) rather than .001₂. This misinterprets which bit is set in the fractional portion and hence is not correct.
Option C:
Option C, 7.5, corresponds to a fractional part of .1₂, where only the 1/2 place is set. This does not align with .001₂, which has only the 1/8 position set.
Option D:
Option D, 7.375, equals 7 + 0.375, which would correspond to fractional bits .011₂. Since the given binary has only the last fractional bit as 1, this value is inconsistent.
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