Digital building blocks: match each component in List I to its primary function in List II. List I (Component) A. Multiplexer B. De-multiplexer C. Shift register D. Encoder List II (Function) Sequential memory (stores and shifts data) Converts decimal (or 1-of-N) input to a binary code Data selector (routes one of many inputs to a single output) Routes a single input to one of many outputs

Introduction / Context:
Digital system design relies on a handful of versatile building blocks. This question tests your understanding of what multiplexers, demultiplexers, shift registers, and encoders do in practical circuits such as data routers, buses, and simple memory elements.

Given Data / Assumptions:

• A multiplexer (MUX) selects one of many inputs under control of select lines.
• A de-multiplexer (DEMUX) routes one input onto one of many outputs under select control.
• A shift register stores bits and shifts them on clock edges, acting as sequential memory.
• An encoder maps a 1-of-N active input to a binary code.

Concept / Approach:

Associate each device with its canonical textbook definition and common use. Think of data direction: MUX is many-to-one (selector), DEMUX is one-to-many (router). A shift register is sequential because it depends on a clock. An encoder reduces many input lines to a smaller set of coded outputs.

Step-by-Step Solution:

Verification / Alternative check:

Draw quick block diagrams: a 4-to-1 MUX chooses among four inputs with two select lines; a 1-to-4 DEMUX drives one selected output line; a 4-bit shift register delays/serializes data; a 10-to-4 encoder outputs a 4-bit BCD code from ten inputs. These align perfectly with the mapping.

Why Other Options Are Wrong:

• Pairing MUX with “one-to-many routing” reverses the data direction (that is DEMUX).
• Calling a shift register a “data selector” ignores its clocked storage/shift behavior.
• Mapping an encoder to “sequential memory” confuses combinational coding with storage.

Common Pitfalls:

Confusing encoders with decoders. A decoder takes a binary code and asserts one of many outputs, whereas an encoder does the opposite. Also, do not conflate DEMUX with decoder—although similar structures appear, the functional role differs: DEMUX routes data, decoder generates enables.

Final Answer:

A-3, B-4, C-1, D-2