UGC NET Questions (Paper – 1)

To convert 110111010101 to decimal, we expand it using powers of two. The bit pattern corresponds to 2^11 + 2^10 + 2^8 + 2^7 + 2^6 + 2^4 + 2^2 + 2^0. This sum is 2048 + 1024 + 256 + 128 + 64 + 16 + 4 + 1 = 3541. Therefore, the decimal equivalent of 110111010101₂ is 3541.

Option A:
Option A, 3521, is smaller than the correct sum. If we re-evaluate the place values, the powers of two do not add up to 3521. This number reflects a slightly different pattern of bits than the one given, so it cannot be correct.

Option B:
Option B, 3540, is just one less than the actual decimal value. A correct conversion must match the exact weighted sum of all set bits. Since the correct expansion yields 3541, this near value is not acceptable.

Option C:
Option C, 3451, changes the hundreds digit significantly. This would require a very different combination of powers of two. Because the given bit pattern clearly sums to 3541, 3451 is inconsistent with the binary representation.

Option D:
Option D, 3541, exactly matches the value obtained from summing the weights of all ones. Both manual calculation and calculator verification confirm this result. Hence, this option correctly represents the decimal value of the given binary number.

To convert 1111100111₂ to decimal, we sum the powers of two corresponding to each 1 bit. The pattern represents 2^9 + 2^8 + 2^7 + 2^6 + 2^5 + 2^2 + 2^1 + 2^0. This gives 512 + 256 + 128 + 64 + 32 + 4 + 2 + 1 = 999. Therefore, the decimal value of 1111100111₂ is 999.

Option A:
Option A, 995, is slightly smaller than the correct sum. If we recompute the place values, the total clearly comes to 999, not 995. Hence, this option does not preserve the exact equality required for base conversion.

Option B:
Option B, 997, is also close but still not equal to 999. A correct binary-to-decimal conversion must yield an exact match. Because the powers of two add up precisely to 999, 997 is not the correct result.

Option C:
Option C, 999, coincides exactly with the sum of all relevant powers of two. Both manual expansion and calculator verification confirm this equality. Thus, it is the correct decimal equivalent of the given binary number.

Option D:
Option D, 1001, exceeds the correct value by 2. It would correspond to a different combination of bits in the binary representation. Therefore, 1001 is not consistent with the pattern 1111100111₂.