Convert the binary number 1011.1101 to its decimal equivalent. Which of the…
2024
Convert the binary number 1011.1101 to its decimal equivalent. Which of the following is the correct decimal value?
Answer: E. None of the above — To convert the binary number 1011.1101 to decimal, split it into integer and fractional parts. Integer part: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1…
- A.
11.75
- B.
12.125
- C.
13.5
- D.
More than one of the above
- E.
None of the above
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Correct answer: E
To convert the binary number 1011.1101 to decimal, split it into integer and fractional parts.
Integer part: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀.
Fractional part: .1101₂ = 1×2⁻¹ + 1×2⁻² + 0×2⁻³ + 1×2⁻⁴ = 0.5 + 0.25 + 0 + 0.0625 = 0.8125₁₀.
Total: 11 + 0.8125 = 11.8125₁₀.
None of the given options (A: 11.75, B: 12.125, C: 13.5) match this value. Therefore, the correct answer is E: None of the above.