Operation to convert binary to decimal – UGC NET Question

Binary numbers are expressed in base 2, so each position corresponds to a power of 2. To convert a binary number to decimal, we multiply each bit by the appropriate power of 2 and add these products. This process accounts for each positional contribution. Therefore, we use powers of 2 in the conversion.

Option A:
Option A, 8, would only be appropriate if we were converting from octal, where the base is 8. Using powers of 8 for binary would give incorrect results.

Option B:
Option B, 10, pertains to decimal positional representation. While the result is expressed in decimal, the positional weights for binary digits must still be powers of 2.

Option C:
Option C, 16, corresponds to hexadecimal, a base-16 system. Hex digits are weighted by powers of 16, not appropriate for direct binary conversion.

Option D:
Option D is correct because binary uses base 2 and each position is 2^n for some integer n. Converting by multiplying bits by powers of 2 is the standard method used in computing.