Past exam of the mathematics course of the University of Cambridge / 2006 / ia / Paper 5 / 10 / e / Solution

Choose bit zero of each integer to represent the leftmost cell in its group of 32 columns. Then use a quotient to choose the word and a remainder to choose the bit:For valid $0\le i,j<1024$, j >>> 5 is $\lfloor j/32\rfloor$ and ranges from zero to 31. The bit mask j & 31 is the offset $j\mathrm{mod}32$. The logical right bit shift brings the desired bit to position zero; the final mask selects only that bit. Even bit 31 of a negative stored word is extracted correctly, because >>> inserts zeros. A different convention, with the leftmost cell in the most significant bit, would instead shift by 31 - (j & 31) and must be used consistently.