Why this topic is important for ECET?
Combinational circuits are the building blocks of digital electronics. Every question in ECET related to logic design, minimization, and digital systems is based on them. Topics like adders, subtractors, multiplexers, decoders, and encoders frequently appear in exams. Mastering these circuits improves your accuracy, speed, and problem-solving ability for competitive exams like ECET, GATE, and even interviews.
📘 Concept Notes
1. What is a Combinational Circuit?
- A combinational circuit is a digital circuit in which the output depends only on the present inputs (no memory).
- Unlike sequential circuits, combinational circuits have no feedback or clock dependency.
Examples:
- Adders
- Subtractors
- Multiplexers
- Demultiplexers
- Encoders
- Decoders
2. Basic Building Blocks
(a) Adders
- Half Adder: Adds 2 bits (A and B).
- Sum = A ⊕ B
- Carry = A · B
- Full Adder: Adds 3 bits (A, B, Cin).
- Sum = A ⊕ B ⊕ Cin
- Carry = AB + BCin + ACin
(b) Subtractors
- Half Subtractor: Subtracts 2 bits (A – B).
- Difference = A ⊕ B
- Borrow = A’ · B
- Full Subtractor: Subtracts 3 bits (A – B – Bin).
- Difference = A ⊕ B ⊕ Bin
- Borrow = A’B + A’Bin + BBin
(c) Multiplexers (MUX)
- Selects one input out of many based on selection lines.
- Example: 4-to-1 MUX uses 2 selection lines.
Equation:
(d) Demultiplexers (DEMUX)
- Opposite of MUX.
- Takes one input and sends it to one of many outputs based on select lines.
(e) Encoders
- Converts 2ⁿ inputs into n outputs.
- Example: 8-to-3 encoder.
(f) Decoders
- Converts n inputs into 2ⁿ outputs.
- Example: 3-to-8 decoder.
3. Simplification using K-Maps
- Boolean functions are simplified using Karnaugh Maps (K-Maps).
- Reduces the number of gates in implementation.
⚙️ Formulas
- Half Adder:
Full Adder:
Half Subtractor:
Full Subtractor:
MUX General Equation:
🔟 10 MCQs
Q1. A half adder has how many inputs and outputs?
a) 1 input, 1 output
b) 2 inputs, 2 outputs
c) 2 inputs, 1 output
d) 3 inputs, 2 outputs
Q2. The sum output of a full adder is given by:
a) AB + BC + AC
b) A ⊕ B ⊕ Cin
c) A + B + Cin
d) (A ⊕ B) Cin
Q3. The borrow expression in a half subtractor is:
a) AB
b) A’B
c) A ⊕ B
d) AB’
Q4. A 4-to-1 multiplexer requires how many select lines?
a) 1
b) 2
c) 3
d) 4
Q5. Which of the following is NOT a combinational circuit?
a) Adder
b) Decoder
c) Flip-Flop
d) Encoder
Q6. The carry expression for a full adder is:
a) AB + BCin + ACin
b) A ⊕ B ⊕ Cin
c) AB’ + A’B
d) (A ⊕ B) Cin
Q7. In a 3-to-8 decoder, the number of output lines is:
a) 3
b) 8
c) 6
d) 2³
Q8. Design a logic expression for a 2-to-1 MUX output:
a) Y = S’A0 + SA1
b) Y = A0A1 + S
c) Y = (A0 + A1)S
d) Y = A0S + A1S’
Q9. If inputs are A=1, B=1, Cin=1 in a full adder, the outputs will be:
a) Sum=1, Carry=1
b) Sum=0, Carry=1
c) Sum=1, Carry=0
d) Sum=0, Carry=0
Q10. A 16-to-1 multiplexer requires how many select lines?
a) 2
b) 3
c) 4
d) 5
✅ Answer Key
| Q No | Answer |
|---|---|
| Q1 | b |
| Q2 | b |
| Q3 | b |
| Q4 | b |
| Q5 | c |
| Q6 | a |
| Q7 | b |
| Q8 | a |
| Q9 | b |
| Q10 | c |
🧠 Explanations
- Q1: Half adder → 2 inputs (A, B), 2 outputs (Sum, Carry).
- Q2: Full adder sum = A ⊕ B ⊕ Cin.
- Q3: Borrow = A’B in half subtractor.
- Q4: 2 select lines required for 4 inputs (2²=4).
- Q5: Flip-flop is sequential, not combinational.
- Q6: Carry expression = AB + BCin + ACin.
- Q7: 3-to-8 decoder → 8 outputs.
- Q8: 2-to-1 MUX output = S’A0 + SA1.
- Q9: For A=1, B=1, Cin=1 → Sum=1⊕1⊕1=0, Carry=1.
- Q10: 16 inputs need 4 select lines (2⁴=16).
🎯 Motivation / Why Practice Matters
Combinational circuits are direct scoring topics in ECET 2026.
- Questions often test truth table, Boolean simplification, or circuit design.
- Speed matters → memorize standard forms of adders, subtractors, MUX, decoders.
- With practice, you can solve these questions in less than 1 minute, giving you an edge in the exam.
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