Each block's structure dictates its use: a-iii, b-iv, c-ii, d-i — option 2.

b is the easiest anchor: "many to one switch" is a literal restatement of what a multiplexer is. Its select lines name which of the inputs reaches the single output, and the whole is a Boolean sum of minterms:

\(Y=\overline{S_{1}}\,\overline{S_{0}}I_{0}+\overline{S_{1}}S_{0}I_{1}+S_{1}\overline{S_{0}}I_{2}+S_{1}S_{0}I_{3}\)

c — why the decoder generates chip selects. It is the multiplexer's dual: n inputs, and exactly one of \(2^{n}\) outputs active for each input code. Feed it the high-order address bits and each output enables one memory device, so a 74138 splits an address space into eight blocks. Since memory CS pins are active low, decoders are built with NAND gates and give active-low outputs — the two conventions were designed to match.

a — parallel to serial. Load all n flip-flops of a shift register at once, then clock n times, and the word leaves the last stage one bit per clock. This is what a UART transmitter does, and it is the general method of converting a wide internal bus to a narrow external link.

d — frequency division. A flip-flop wired to toggle needs two input edges for one output cycle, so each stage halves the frequency and n stages divide by \(2^{n}\). "Counting" and "dividing" are the same operation viewed differently — the count is the state, the division is the rate at which the top bit changes.

The multiplexer and shift register are close cousins, which is why a is worth checking against b: a MUX driven by a counter also converts parallel to serial, but it is combinational and needs the counter to sequence it, whereas a shift register does the job by itself with a single clock.

Hence, the correct code is a-iii, b-iv, c-ii, d-i.