Question

Given the following Lists:

Identify the correct match.

• A. a-ii; b-i; c-iii; d-iv
• B. a-i; b-ii; c-iv; d-iii
• C. a-iii; b-i; c-iv; d-ii
• D. a-iv; b-i; c-ii; d-iii

Hint:

Be careful when converting between different number bases. For one's complement, simply flip the bits.

Answer 1

The Correct Option is C

We need to convert each number in List-I to a common base (decimal is convenient) and then match it with the equivalent value in List-II. a. \( 10101_{(2) \) to Decimal:}
\( 1 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 = 16 + 0 + 4 + 0 + 1 = 21_{(10)} \)
Match: a - iii b. \( DAD_{(16) \) to Decimal:}
In hexadecimal, A=10, D=13.
\( 13 \cdot 16^2 + 10 \cdot 16^1 + 13 \cdot 16^0 = 13 \cdot 256 + 10 \cdot 16 + 13 \cdot 1 = 3328 + 160 + 13 = 3501_{(10)} \)
Now, convert \( 3501_{(10)} \) to octal (base-8):
\( 3501 \div 8 = 437 \) remainder \( 5 \)
\( 437 \div 8 = 54 \) remainder \( 5 \)
\( 54 \div 8 = 6 \) remainder \( 6 \)
\( 6 \div 8 = 0 \) remainder \( 6 \)
So, \( 3501_{(10)} = 6655_{(8)} \)
Match: b - i
c. One's (complement) of \( 1101_{(2) \):}
The one's complement of a binary number is obtained by inverting all the bits (0 becomes 1, and 1 becomes 0).
One's complement of \( 1101_{(2)} \) is \( 0010_{(2)} \) Match: c - iv
d. \( 401_{(8) \) to Decimal:}
\( 4 \cdot 8^2 + 0 \cdot 8^1 + 1 \cdot 8^0 = 4 \cdot 64 + 0 \cdot 8 + 1 \cdot 1 = 256 + 0 + 1 = 257_{(10)} \)
Now, convert \( 257_{(10)} \) to hexadecimal (base-16):
\( 257 \div 16 = 16 \) remainder \( 1 \)
\( 16 \div 16 = 1 \) remainder \( 0 \)
\( 1 \div 16 = 0 \) remainder \( 1 \)
So, \( 257_{(10)} = 101_{(16)} \)
Match: d - ii
Combining the matches:
a - iii
b - i
c - iv
d - ii
This corresponds to option (3).