Question

Consider following numbers :
A. $(1101.01)_{2} = (13.25)_{10}$

B. $(13.28)_{10} = (1101.011)_{2}$

C. $(2\text{A})_{16} = (42)_{10}$

D. $(37)_{8} = (11010)_{2}$

Choose the correct answer from the options given below :

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

Hint:

For base-8 to base-2, convert each octal digit to 3 bits: $3 \to 011$, $7 \to 111$. So $37_8 = 011111_2 = 31_{10}$.

Answer 1

The Correct Option is D

We evaluate the truth of each numerical conversion statement individually. 1. Evaluating Statement A: $(1101.01)_2 = (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) + (0 \times 2^{-1}) + (1 \times 2^{-2})$ $= 8 + 4 + 0 + 1 + 0 + 0.25 = 13.25$. Statement A is correct. 2. Evaluating Statement B: From A, we know $13.25_{10} = 1101.01_2$. The decimal part $0.28$ cannot be represented by three binary digits $.011$ (which is $0.25 + 0.125 = 0.375$). Statement B is incorrect. 3. Evaluating Statement C: $(2\text{A})_{16} = (2 \times 16^1) + (10 \times 16^0) = 32 + 10 = 42$. Statement C is correct. 4. Evaluating Statement D: $(37)_8 = (3 \times 8^1) + (7 \times 8^0) = 24 + 7 = 31$. $(11010)_2 = 16 + 8 + 2 = 26$. $31 \neq 26$. Statement D is incorrect. Conclusion: Only A and C are correct.