6.10 Demultiplexer: Routing One Input to a Selected Output

Explain how a demultiplexer routes a single data input to exactly one of several outputs based on select-line values, and describe its structural relationship to the multiplexer as its functional inverse.

A demultiplexer (DEMUX) performs the inverse operation of a multiplexer: rather than selecting one of many inputs to route to a single output, a DEMUX takes a single input signal and routes it to exactly one of several possible outputs, chosen by the binary value on its select lines. Wherever a multiplexer is used to combine multiple sources down to one shared line, a demultiplexer is typically used at the receiving end to distribute that shared line's signal back out to the correct individual destination.

One input routed to one selected output

A demultiplexer has a single data input, a set of select lines, and 2^n outputs (for n select lines) — the same 2^n relationship seen in the multiplexer, but applied to outputs instead of inputs. For any given select-line combination, exactly one output carries the value of the data input, while every other output is held at a fixed inactive value (typically 0).

This structural symmetry with the multiplexer is intentional: internally, a demultiplexer is built from a set of AND gates, one per output, each gated by a unique combination of the select lines (exactly analogous to the MUX's AND-gate structure) and by the single shared data input — only the AND gate matching the current select-line combination passes the data input through to its corresponding output; every other AND gate outputs 0 because its select-line gating condition is not satisfied.

Worked structure: 1 input, 2 select lines, 4 outputs

A DEMUX with 2 select lines and 4 outputs takes a single data input and, depending on the 2-bit select-line value, routes that input to exactly one of its four outputs (Y0, Y1, Y2, or Y3), while the other three outputs remain inactive. This is precisely the structure named in the spec: 1 input, 2 select lines, 4 outputs, with one output active based on the select value.

Extending this pattern, a DEMUX with n select lines always produces 2^n outputs, following the identical power-of-two relationship used throughout multiplexer and demultiplexer design — whether n select lines are being used to choose among 2^n inputs (as in a MUX) or to route to 2^n outputs (as in a DEMUX).

Demultiplexer structure

1 data input
n select lines
2^n outputs

For any select-line value, exactly one output = data input; every other output = 0 (inactive).

Code Examples

This matches the spec's described structure directly: 1 input, 2 select lines, 4 outputs, with exactly one output active based on the select value. Here select code 10 (decimal 2) routes DIN specifically to output Y2, while the other three outputs stay at their inactive value of 0 regardless of what DIN is. Expected result: Y2 = DIN, all other outputs = 0

Select lines S1S0=10 route the single data input exclusively to output Y2; all other outputs remain 0.

Data input: DIN = 1
Select lines S1 S0 = 10  (decimal 2)

Outputs:
  Y0 = 0   (select code does not match 00)
  Y1 = 0   (select code does not match 01)
  Y2 = DIN = 1   (select code matches 10)
  Y3 = 0   (select code does not match 11)

Only Y2 carries the data input's value; every other output is held at 0.

1-to-4 demultiplexer block diagram

A demultiplexer routes a single input to exactly one of 2^n outputs, selected by n select lines.

,---> Y0
                        |
  DIN ---- [ DEMUX ] ---+---> Y1
             |          |
           S1 S0        +---> Y2
                         |
                         '---> Y3

  For any (S1,S0) value, exactly one Yi = DIN; all other outputs = 0.

Important Rules

A demultiplexer has 1 data input, n select lines, and 2^n outputs.

For any select-line value, exactly one output carries the data input's value; all others are inactive (0).

The demultiplexer is the structural and functional inverse of the multiplexer: DEMUX distributes one signal to many possible destinations, while MUX combines many possible sources into one.

Where demultiplexers are used

Demultiplexers are commonly paired with multiplexers at opposite ends of a shared communication channel — a MUX combines several signal sources onto one shared line for transmission, and a DEMUX at the receiving end separates that shared line back out to the correct individual destination, based on the same select-line (or timing) information used on the sending side. Demultiplexers also appear directly in memory addressing (routing a data value to one of several memory locations based on an address) and in control logic that must activate exactly one of several downstream circuits based on a binary control code.

Block Diagram

2ⁿ Output Channels n Control Signals A demultiplexer is the multiplexer's mirror image: one incoming data channel fans back out to 2ⁿ possible output lines, with the same n select (control) lines now deciding which single output line actually receives that data.

Confusing a demultiplexer with a multiplexer, or assuming they perform the same operation just described differently.

Keep the direction of data flow straight: a multiplexer has many inputs and one output (selects which input to use); a demultiplexer has one input and many outputs (selects which output to route to).

Although both circuits use select lines and share a similar AND-gate-plus-select-line internal structure, their data flow directions are opposite — a MUX narrows many signals down to one, while a DEMUX widens one signal out to many possible destinations.

What is the correct structural relationship between a multiplexer and a demultiplexer? A. A multiplexer routes many inputs to one output; a demultiplexer routes one input to many possible outputs — they are functional inverses of each other B. They perform an identical operation; the two names are just synonyms C. A demultiplexer requires a clock signal, while a multiplexer does not D. A multiplexer is used only for arithmetic circuits, while a demultiplexer is used only for memory circuits

A. A multiplexer routes many inputs to one output; a demultiplexer routes one input to many possible outputs — they are functional inverses of each other — A multiplexer selects one of several data inputs to route to a single output; a demultiplexer takes a single input and routes it to one of several possible outputs, based on select-line values. They are structural and functional inverses of one another, both governed by the same 2^n select-line-to-port-count relationship.

For a 1-to-4 demultiplexer with select lines S1S0=10 and data input DIN=1, which output is active? A. Y2, since select code 10 (decimal 2) corresponds to output index 2 B. Y0, since demultiplexers always default to the first output C. All four outputs simultaneously, since DIN=1 is broadcast to every output D. Y3, since 10 is interpreted as the highest available select code

A. Y2, since select code 10 (decimal 2) corresponds to output index 2 — The select-line value directly encodes the output index in binary: S1S0=10 is decimal 2, so output Y2 becomes active and carries DIN's value (1), while Y0, Y1, and Y3 remain at their inactive value of 0.

A 1-to-8 demultiplexer is needed. How many select lines are required, and what does each of the 8 outputs represent?

3 select lines are required, since 2^3 = 8. Each of the 8 outputs (Y0 through Y7) represents one possible destination for the single data input; for any given 3-bit select-line value, exactly one of the 8 outputs carries the data input's value, while the remaining seven stay at 0.

Apply the same 2^n relationship used for multiplexers, but for outputs instead of inputs.