Binary equivalent of 1234 decimal – UGC NET Question

To write 1234 in binary, we express it as a sum of powers of 2 or apply repeated division by 2. The expansion 1234 = 1024 + 128 + 64 + 16 + 2 corresponds to setting bits at those positions and clearing others. This gives the binary sequence 10011010010₂ with no leading zeroes. Therefore, option B is the correct binary representation of 1234.

Option A:
Option A differs in some middle bits, corresponding to a combination of powers of 2 that sums to a value slightly less than 1234. Because its positional weights do not match the required expansion, it cannot represent 1234.

Option B:
Option B matches exactly the powers of 2 needed to sum to 1234 and has no unnecessary leading zeros, giving the minimum-length representation. Its pattern of ones and zeros correctly encodes 1024 + 128 + 64 + 16 + 2. That is why it is the correct answer.

Option C:
Option C changes one of the bits that should be set to represent 1234, resulting in a different sum of powers of 2. The decimal value obtained is lower than 1234, making this option incorrect.

Option D:
Option D sets an extra bit compared to the correct representation, which increases the decimal value beyond 1234. As a result, it cannot be the right binary encoding of 1234.