The decimal equivalent of the binary number (1011.011)2 is ________

Question

BlackTom AI · Accepted Answer

Question restatement: The decimal equivalent of the binary number (1011.011)2 is ________.

Option analysis:
- Option a: (11.375)10
  This matches the correct conversion. The integer part 10112 equals 8+2+1 = 11. The fractional part .0112 equals 0*(1/2) + 1*(1/4) + 1*(1/8) = 0 + 0.25 + 0.125 = 0.375. Adding them gives 11.375 in base 10.
- Option b: (9.23)10
  This is incorrect because the integer portion 9 would require the binary representation 1001 for the whole number, and the fractional digits do not align with standard binary fractions. Moreover, 0.23 is not a direct binary fraction representation for 0.011 in base 2.
- Option c: (11.175)10
  The integer part 11 is plausible, but the fractional part 0.175 does not correspond to the binary fraction .011. Since .0112 equals 0.375, not 0.175, this option miscalculates the fractional value.
- Option d: (10.123)10
  This option is incorrect because the integer portion 10 suggests a binary value of 1010, whereas the given binary is 1011. The decimal fraction 0.123 does not align with the actual binary fraction .011, further confirming this mismatch.

Summary: The only option that faithfully converts both the integer and fractional parts of 1011.0112 to base 10 is 11.375, so option a is the correct representation.

FIT1047_S1_2025 Week 1 quiz

The decimal equivalent of the binary number (1011.011)2 is ________

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