Demultiplexers

WHAT is a Demultiplexer?

WHY does it exist? In real hardware you often have one shared signal (a serial data stream, a bus line, a clock) and you must deliver it to one selected destination — a specific register, memory row, or peripheral. The DEMUX is the physical "address decoder + gate" that does this.

HOW it works — derive it from scratch

Take the simplest useful case: a 1-to-2 DEMUX ( $n=1$ , one select line $S$ ).

Step 1 — What do we want?

If $S=0$ : send $D$ to $Y_0$ , force $Y_1=0$ .
If $S=1$ : send $D$ to $Y_1$ , force $Y_0=0$ .

Why this step? We list the desired behaviour before touching gates — this is the truth table, our contract.

$S$	$D$	$Y_0$	$Y_1$
0	0	0	0
0	1	1	0
1	0	0	0
1	1	0	1

Step 2 — Read the logic straight off the table. $Y_0$ is $1$ only when $S=0$ AND $D=1$ . $Y_1$ is $1$ only when $S=1$ AND $D=1$ .

$Y_0 = \overline{S}\,D \qquad Y_1 = S\,D$

Why this step? Each output is an AND of the data with the correct combination of select lines — exactly $D$ gated by the "am I the chosen one?" condition.

Step 3 — Generalise to $2^n$ outputs. Each output $Y_k$ fires only when the select lines spell the number $k$ in binary. Let $m_k$ be that select-decode term (a minterm of the select lines). Then:

Worked Examples

Common Mistakes

Active Recall

Recall Explain to a 12-year-old (Feynman)

Imagine a train station with ONE incoming track and 8 platforms. A signalman looks at a number card (the select lines) and flips a switch so the incoming train rolls onto exactly the platform matching that number. All the other platforms stay empty. The train itself is your data bit — if no train comes (data = 0), even the chosen platform is empty. That signalman is the demultiplexer: one input, many outputs, and a "number card" that picks the destination.

Flashcards

What does a demultiplexer do?

Routes one data input to exactly one of

2^n

outputs, chosen by

n

select lines.

How many outputs does a 1-to-

2^n

DEMUX have and how many select lines?

2^n

outputs,

n

select lines.

Write the output equation for output

Y_k

of a DEMUX.

Y_k = D\cdot m_k

, where

m_k

is the minterm of the select lines equal to 1 only for code

k

Give

Y_0

and

Y_1

for a 1-to-2 DEMUX with select

S

Y_0=\overline{S}D

Y_1=SD

How do you turn a DEMUX into a decoder?

Tie the data input

D=1

; then each

Y_k=m_k

, the decoder output.

For a 1-to-4 DEMUX with

D=1

S_1S_0=11

, which output is high?

Y_3

(binary 11 = decimal 3), all others 0.

What is the difference between a MUX and a DEMUX?

MUX = many inputs → one output (

Y=\sum D_k m_k

); DEMUX = one input → many outputs (

Y_k=D\,m_k

If the data input

D=0

, what are all DEMUX outputs?

All outputs are 0, regardless of select lines.

Why is each non-selected output 0?

Its minterm

m_k=0

, so

Y_k=D\cdot0=0

Connections

Multiplexers — the exact inverse operation (many-in-one-out).
Decoders — a DEMUX with data tied to 1 IS a decoder.
Minterms and SOP — each output uses a select-line minterm.
Encoders — reverse of decoders, related family.
Memory Addressing — DEMUX/decoders select which memory word/row is driven.
Bus Systems — one bus line distributed to multiple destinations.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Demultiplexer ko simple tarike se samjho: ye ek "router" hai jiske paas sirf EK data input hota hai, lekin bahut saare outputs ( $2^n$ ) hote hain. Kaunse output pe data jaayega, ye decide karte hain select lines. Jaise ek railway signalman ek number card dekhta hai aur incoming train ko usi platform pe bhej deta hai — baaki platforms khaali reh jaate hain. Wahi kaam DEMUX karta hai.

Formula bilkul seedha derive hota hai. Har output $Y_k$ tabhi ON hota hai jab select lines exactly $k$ ka binary code banayein AND data $D=1$ ho. Isliye $Y_k = D \cdot m_k$ , jahan $m_k$ select lines ka minterm hai. Agar $D=0$ ho, to chosen output bhi $0$ rahega — DEMUX apni marzi se $1$ nahi banata, bas data ko faithfully aage bhejta hai.

Ek important connection yaad rakho: agar tum $D=1$ permanently laga do, to DEMUX bilkul ek decoder ban jaata hai. Yani same hardware, thoda alag use. Aur DEMUX bilkul MUX ka ulta hai — MUX many-in one-out karta hai, DEMUX one-in many-out.

Exam me sabse common galti: log soch lete hain ke $n$ select lines matlab $n$ outputs. Nahi! $n$ select lines matlab $2^n$ outputs (3 selects → 8 outputs). Aur select bits ko decimal me convert karna mat bhoolna — $S_1S_0 = 10$ ka matlab decimal 2, isliye $Y_2$ active hoga.

WHAT is a Demultiplexer?

HOW it works — derive it from scratch

Worked Examples

Common Mistakes

Active Recall

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Combinational Circuits

Connections