The S'R' latch is a programmable memory: we can tell it what to remember. Programming is accomplished by sending a sequence of S'R' logic input value pairs to the latch. For example, sending the S'R' pair 11 at time = t commands the latch to output at time t+1 the value Q(t+1) that is equal to the value at time t, Q(t). In other words, S'R' = 11 is the command to "Keep remembering the current Q(t) logic value." The command S'R' = 01 at time t = 0 commands the latch to begin remembering a logic 1 value regardless of the logic value that may have been the current memory. That is, 01 commands Q(t+1)= 1, regardless of the value of Q(t). A sequence of commands sent to an S'R' latch constitutes a program for the latch. The behavior of the latch from the first command of the sequence to the final command of the sequence represents the execution of the latch program. a) Write an S'R' latch program that will cause the Q output waveform to include exactly one a rising edge. List the program commands one per line, just as you would write the lines of any program. b) How many S'R' latches are needed to build a register that can hold the symbol string for the unsigned integer 127 stored in the unary system? c) How many S'R' latches are needed to build a register that can hold the symbol string for the unsigned integer 127 stored in the weighted positional base 2 system?