Demultiplexers — Hinglish notes

3.3.6 · Hardware › Combinational Circuits

DEMUX KYA hota hai?

Yeh exist KYU karta hai? Real hardware mein aksar aapke paas ek shared signal hota hai (serial data stream, bus line, ya clock) aur aapko use ek selected destination tak deliver karna hota hai — ek specific register, memory row, ya peripheral. DEMUX woh physical "address decoder + gate" hai jo yeh kaam karta hai.

HOW yeh kaam karta hai — scratch se derive karo

Sabse simple useful case lete hain: ek 1-to-2 DEMUX ( $n = 1$ , ek select line $S$ ).

Step 1 — Hum kya chahte hain?

Agar $S = 0$ : $D$ ko $Y_{0}$ par bhejo, $Y_{1} = 0$ force karo.
Agar $S = 1$ : $D$ ko $Y_{1}$ par bhejo, $Y_{0} = 0$ force karo.

Yeh step kyun? Hum gates touch karne se pehle desired behaviour list karte hain — yeh truth table hai, hamara 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 — Table se seedha logic padho. $Y_{0}$ tab $1$ hota hai jab sirf $S = 0$ AND $D = 1$ . $Y_{1}$ tab $1$ hota hai jab sirf $S = 1$ AND $D = 1$ .

$Y_{0} = \overline{S} D Y_{1} = S D$

Yeh step kyun? Har output, data ka select lines ke sahi combination ke saath AND hota hai — exactly $D$ jo "kya main chosen one hun?" condition se gate hota hai.

Step 3 — $2^{n}$ outputs tak generalise karo. Har output $Y_{k}$ tab fire karta hai jab select lines binary mein number $k$ spell karti hain. Maano $m_{k}$ woh select-decode term hai (select lines ka ek minterm). Tab:

Worked Examples

Common Mistakes

Active Recall

Recall 12-saal ke bachche ko explain karo (Feynman)

Socho ek train station jisme EK aane wala track hai aur 8 platforms hain. Ek signalman ek number card (select lines) dekhta hai aur switch flip karta hai taaki aane wali train exactly us platform par jaye jo us number se match karta ho. Baaki saare platforms khaali rehte hain. Train khud tumhara data bit hai — agar koi train nahi aati (data = 0), toh chosen platform bhi khaali hai. Woh signalman demultiplexer hai: ek input, kaafi saare outputs, aur ek "number card" jo destination choose karta hai.

Flashcards

Demultiplexer kya karta hai?

Ek data input ko

2^{n}

outputs mein se exactly ek par route karta hai, jo

n

select lines choose karti hain.

Ek 1-to-

2^{n}

DEMUX mein kitne outputs aur kitni select lines hoti hain?

2^{n}

outputs,

n

select lines.

DEMUX ke output

Y_{k}

ke liye output equation likho.

Y_{k} = D \cdot m_{k}

, jahan

m_{k}

select lines ka minterm hai jo sirf code

k

ke liye 1 hota hai.

Select

S

ke saath 1-to-2 DEMUX ke liye

Y_{0}

aur

Y_{1}

likho.

Y_{0} = \overline{S} D

Y_{1} = S D

DEMUX ko decoder mein kaise turn karte hain?

Data input

D = 1

tie kar do; tab har

Y_{k} = m_{k}

ho jaata hai, jo decoder output hai.

1-to-4 DEMUX mein

D = 1

S_{1} S_{0} = 11

ke liye kaun sa output high hai?

Y_{3}

(binary 11 = decimal 3), baaki sab 0.

MUX aur DEMUX mein kya fark hai?

MUX = kaafi saare inputs → ek output (

Y = \sum D_{k} m_{k}

); DEMUX = ek input → kaafi saare outputs (

Y_{k} = D m_{k}

Agar data input

D = 0

ho toh saare DEMUX outputs kya hain?

Saare outputs 0 hain, select lines chahe kuch bhi hon.

Har non-selected output 0 kyun hoti hai?

Uska minterm

m_{k} = 0

hota hai, isliye

Y_{k} = D \cdot 0 = 0

Connections

Multiplexers — exact inverse operation (many-in-one-out).
Decoders — data 1 se tied DEMUX IS ek decoder hai.
Minterms and SOP — har output ek select-line minterm use karta hai.
Encoders — decoders ka reverse, related family.
Memory Addressing — DEMUX/decoders choose karte hain kaun sa memory word/row drive hoga.
Bus Systems — ek bus line kaafi saare destinations mein distribute hoti hai.