Question

The decimal equivalent of the binary number 10011.1 is

• A. 19.50
• B. 11001.11
• C. 5005.55
• D. 19.10

Hint:

Binary digits after decimal are negative powers of 2.

Answer 1

The Correct Option is A

To convert the binary number 10011.1 into its decimal equivalent, we break it into two parts: the integral part (10011) and the fractional part (0.1). Each part is converted separately and then combined to get the final result.

1. Converting the Integral Part (10011) to Decimal:
   • The binary number 10011 can be expressed in terms of powers of 2 as follows:
   • \(1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
   • Calculating each term:
     • \(1 \times 2^4 = 16\)
     • \(0 \times 2^3 = 0\)
     • \(0 \times 2^2 = 0\)
     • \(1 \times 2^1 = 2\)
     • \(1 \times 2^0 = 1\)
   • Adding these gives: \(16 + 0 + 0 + 2 + 1 = 19\)
2. Converting the Fractional Part (0.1) to Decimal:
   • The fractional binary number (0.1) can be expressed in terms of negative powers of 2:
   • \(1 \times 2^{-1}\)
   • Calculating:
     • \(1 \times 2^{-1} = 0.5\)
3. Combining the Integral and Fractional Parts:
   • By combining the decimal integral part (19) with the decimal fractional part (0.5), we get:
   • \(19 + 0.5 = 19.5\)
4. Conclusion:
   • The decimal equivalent of the binary number 10011.1 is 19.5, which corresponds to the correct answer: 19.50.