Binary of decimal 156 – UGC NET Question

Decomposing 156 yields 156 = 128 + 16 + 8 + 4, corresponding to bits in positions 7, 4, 3, and 2. Writing 1s in these positions and 0s elsewhere gives 10011100₂. Therefore, 10011100₂ is the binary form of 156.

Option A:
Option A accurately reflects the sum of powers of 2 equal to 156, using the positions for 2⁷, 2⁴, 2³, and 2². The resulting pattern converts back to 128 + 16 + 8 + 4, which is 156.

Option B:
Option B, 10011010₂, equals 128 + 16 + 8 + 2 = 154, which is slightly less than 156 and thus not correct.

Option C:
Option C, 10010110₂, represents 128 + 16 + 4 + 2 = 150, which is further from 156.

Option D:
Option D, 10011110₂, equals 128 + 16 + 8 + 4 + 2 = 158, overshooting the required value.