Convert the binary number 1011.1101 to its decimal equivalent. Which of the following is the correct decimal value?

Correct Answer (Detailed Explanation is Below)

E. None of the above

Detailed Explanation

Explanation:

To convert binary 1011.1101₂ to decimal, use powers of 2.

 Integer part (1011)

$$1\times2^3 + 0\times2^2 + 1\times2^1 + 1\times2^0$$$$= 8 + 0 + 2 + 1 = 11$$

 Fraction part (.1101)

$$1\times2^{-1} + 1\times2^{-2} + 0\times2^{-3} + 1\times2^{-4}$$$$= 0.5 + 0.25 + 0 + 0.0625 = 0.8125$$

Total decimal value

$$11 + 0.8125 = 11.8125$$

Final Result

Decimal = 11.8125

Check options

• (A) 11.75 ❌

• (B) 12.125 ❌

• (C) 13.5 ❌

✔ Correct answer: (E) None of the above.