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

Correct option is E

To convert the binary number 1011.1101 to decimal, we separate it into integer (1011) and fractional (1101) parts and convert them separately.
· Integer part (1011 in binary to decimal):
· $$1 \times 2^3 = 8$$​​
· $$0 \times 2^2 = 0$$​​
· $$1 \times 2^1 = 2$$​​
· $$1 \times 2^0 = 1$$​​
· Total = 8 + 0 + 2 + 1 = 11
· Fractional part (0.1101 in binary to decimal):
· $$1 \times 2^{-1} = 0.5$$​​
· $$1 \times 2^{-2} = 0.25$$​​
· $$0 \times 2^{-3} = 0$$​​
· $$1 \times 2^{-4} = 0.0625$$​​
· Total = 0.5 + 0.25 + 0 + 0.0625 = 0.8125
· Final Decimal Value:
​$$1011.1101_2 = 11 + 0.8125 = 11.8125_{10}$$​​
Since 11.8125 is not in the given options, the correct answer is (e) None of the above.
Important Key Points:
1. Binary to Decimal Conversion Rule:
· Convert the integer part by multiplying each bit by powers of 2.
· Convert the fractional part by multiplying each bit by negative powers of 2.
2. Decimal Value Calculation:
· Integer part: 1011 (binary) → 11 (decimal)
· Fractional part: 0.1101 (binary) → 0.8125 (decimal)
· Final value: 11.8125 (decimal)
3. Common Binary Fraction Conversions:
· 0.1 (binary) → 0.5 (decimal)
· 0.01 (binary) → 0.25 (decimal)
· 0.001 (binary) → 0.125 (decimal)
· 0.0001 (binary) → 0.0625 (decimal)
Knowledge Booster:
· Binary fractions follow the same conversion rule as whole numbers, but use negative powers of 2 for decimal places.
· Computers use floating-point representation to store non-integer binary values efficiently.
· Fixed-point representation is another method used in digital signal processing (DSP) for fractional binary numbers.
· Binary rounding errors can occur in floating-point arithmetic due to limited precision in digital computation.
· Hexadecimal (base-16) provides a more compact way to represent binary fractions in modern computing.