Combinational circuits ka concept aaj ke digital electronics ke world mein bahut hi important hai. Yeh circuits woh logic circuits hote hain jinmein output sirf inputs ke current state pe depend karta hai, na ki kisi purani state ya memory element pe. Matlab, agar aap inputs change karte ho, to output turant hi change ho jata hai, bina kisi delay ke jo memory elements introduce karte hain. Simple words mein, agar ABC inputs hain, to output = f(A,B,C) jaisa koi pure logic function jisse predict kar pao ki current values ke basis pe output kya hoga.

1. Basic Definitions aur Trick

Combinational circuits ko samajhne ke liye pehle kuch basic definitions yaad rakhna zaruri hai:

  • Input Variables: Jo signals circuit ko feed kiye jaate hain (jaise A, B, C etc.).
  • Output Variables: Resultant signals jo circuit nikalta hai (jaise Y, Z etc.).
  • Logic Function: Mathematical representation of output in terms of inputs (example Y = A AND B + C').

Trick: "Aapne pizza banaya, ingredients (=inputs) ke combination se final pizza (=output) banta hai, bas wahi combinational circuits ka funda hai."

2. Common Gates aur Unke Symbols

Sabse common logic gates hain: AND, OR, NOT, NAND, NOR, XOR, XNOR. Inke symbols bahut hi simple dikhte hain, par jab aap multiple gates ko combine karte ho, toh kaafi interesting behavior milta hai.

2.1 AND Gate

Output tabhi HIGH (1) hoga jab saare inputs HIGH honge. Trick: "AND matlab Aur, sabhi chahiye!"

2.2 OR Gate

Output HIGH jab koi ek input HIGH ho. Trick: "OR matlab ya, koi ek chalega!"

3. Standard Combinational Circuits

Byjus notes mein discuss kiye gaye main combinational circuits ye hain:

  • Multiplexer (MUX)
  • Demultiplexer (DEMUX)
  • Encoder
  • Decoder
  • Adder aur Subtractor
  • Comparator

3.1 Multiplexer (MUX)

Multiplexer chhota selector device jaisa hai jo bahut saare inputs me se sirf ek input select karke output deta hai. Jaise 4-to-1 MUX mein 4 data inputs hote hain (D0-D3) aur 2 select lines (S0,S1). Select lines decide karti hain kaunsa input output pe pass hoga.

Shortcut Trick: "MUX = Mix + U + X, pick(UP) ek input mix kara do X marking se!"

3.2 Demultiplexer (DEMUX)

Demultiplexer MUX ka reverse hota hai. Ek input ko multiple outputs me route karta hai based on select lines.

Short Trick: "DE-MUX, Distribute Everywhere—one input, Many outputs!"

3.3 Encoder

Encoder input code se smaller output code produce karta hai. For example, 8-to-3 encoder mein 8 inputs, 3 outputs. Jo input active hoga, uska binary code outputs pe milega.

3.4 Decoder

Decoder encoder ka opposite: binary code input deta hai, aur us corresponding single output line ko HIGH karta hai.

3.5 Adder/Subtractor

Binary addition/subtraction karne wala circuit. Full Adder ek single-bit addition karta hai, jisme input bits plus carry-in hota hai, aur carry-out generate hota hai.

4. Design Steps

Combinational circuit design karne ke steps kuch is tarah hote hain:

  1. Problem statement clearly define karo.
  2. Inputs aur outputs list banao.
  3. Truth table draw karo.
  4. Simplification karne ke liye Boolean expression derive karo (K-map ya algebraic method).
  5. Logic gate level diagram draw karo.

5. Simplification Techniques

K-map (Karnaugh Map) ek popular method hai boolean simplification ke liye. 2, 3, 4 variable K-maps sabse common hain.

Memory Trick: "K-Map—K for Karnaugh, K for Keep grouping same terms in bloques!"

6. Real-world Examples

1. Elevator Control: Input sensors (floor buttons) aur select lines decide karti hain elevator ka movement—yeh ek combinational logic plus sequential memory bhi combine hota hai.

2. Traffic Light Controller: Various sensor inputs aur timer signals se next light state decide hota hai.

7. Common Short Tricks

  • "AND = Aur (SAB), OR = Ya (EK)", yaad raho Hindi words se.
  • K-map grouping ko "Block banao, circle maro, solution lao"
  • "Truth table banao, simplify karo, circuit banao"—teen step mantra.

8. Practice Problems

1. Design a 4-to-1 MUX using minimum gates.

2. Simplify the boolean function F(A,B,C,D) = Σ(0,2,5,7,8,10,13,15) using 4-variable K-map.

3. Implement a 4-bit binary adder using full adders.

Conclusion

Combinational circuits basic building blocks hain digital electronics ke. Inke concepts clear hone par aap complex systems like ALU, multiplexers, decoders easily design kar sakte ho. Upar diye short tricks yaad raho aur practice zyada karo!