Question

Arrange the following numbers in ascending order:
A. (10110.011)\(_2\)
B. (32)\(_{10}\)
C. (5F.8)\(_{16}\)
D. F\(_{16}\)
Choose the Correct answer from the options given below:

• A. A, B, C, D
• B. D, A, B, C
• C. B, A, D, C
• D. C, B, D, A

Hint:

To compare numbers in different bases (binary, decimal, hexadecimal), the most reliable method is to convert all of them to a single base, usually decimal. Remember the positional values are powers of the base (2, 10, or 16).

Answer 1

The Correct Option is B

Step 1: Convert all numbers to a common base (decimal is easiest). - A. (10110.011)\(_2\): \[ (1 \cdot 2^4) + (0 \cdot 2^3) + (1 \cdot 2^2) + (1 \cdot 2^1) + (0 \cdot 2^0) + (0 \cdot 2^{-1}) + (1 \cdot 2^{-2}) + (1 \cdot 2^{-3}) \] \[ = 16 + 0 + 4 + 2 + 0 + 0 + 0.25 + 0.125 = 22.375_{10} \] - B. (32)\(_{10}\): This is already in decimal. Value is \(32_{10}\). - C. (5F.8)\(_{16}\): \[ (5 \cdot 16^1) + (F \cdot 16^0) + (8 \cdot 16^{-1}) \] \[ = (5 \cdot 16) + (15 \cdot 1) + (8 / 16) = 80 + 15 + 0.5 = 95.5_{10} \] - D. F\(_{16}\): \[ F_{16} = 15_{10} \]
Step 2: Compare the decimal values. The decimal values are: - A = 22.375 - B = 32 - C = 95.5 - D = 15
Step 3: Arrange them in ascending order. The smallest value is D (15), followed by A (22.375), then B (32), and the largest is C (95.5). The ascending order is D, A, B, C.