The isolated-1-shift-leftoperation (i1sl for short) applied to a binary string S moves a 1 bit by one position to the left in the solution if the bit is not adjacent to any other 1s (i.e., 0s on both sides, or if it is the least-significant bit, a 0 immediately above it).

For instance,

• 010 100, 011 011, 01010 10100

Build a simplified circuit (using only AND, OR, NOT gates) whose output is the ith bit of the i1sl, where1 < i < k 1.