In the ECET 2026 CSE exam, one of the most commonly asked topics in Digital Electronics is Number Systems & Conversions. Whether it’s converting binary to decimal or solving hexadecimal logic, this chapter helps students score quickly and accurately. It’s highly likely to get direct MCQs from this topic, making it perfect for easy revision and scoring. Let’s explore this with crisp notes and 10 ECET-style MCQs with answers and explanations.
📘 Concept Notes – Number Systems & Conversions
🔢 Types of Number Systems:
- Decimal (Base-10)
- Digits: 0–9
- Example: 245₁₀
- Binary (Base-2)
- Digits: 0, 1
- Example: 1101₂
- Octal (Base-8)
- Digits: 0–7
- Example: 57₈
- Hexadecimal (Base-16)
- Digits: 0–9 and A–F (A=10, F=15)
- Example: 1F₁₆
🔄 Conversions:
✅ Binary to Decimal:
Multiply each bit with powers of 2 and add.
Example:
1010₂ = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10₁₀
✅ Decimal to Binary:
Divide by 2 and write remainders in reverse.
Example:
10₁₀ ÷ 2 = 5 R0 → 2 R1 → 1 R0 → 0 R1 → Binary = 1010₂
✅ Binary to Hexadecimal:
Group bits in 4s from right and convert.
Example:
11011011₂ = 1101 1011 → D B → DB₁₆
✅ Hexadecimal to Binary:
Convert each hex digit to 4-bit binary.
Example:
A₁₆ = 1010₂
🧠 Key Concepts:
- Binary uses powers of 2
- Hexadecimal uses powers of 16
- Always write base to avoid confusion (e.g., 25₁₀ ≠ 25₁₆)
- Binary addition follows:
- 0+0 = 0
- 1+0 = 1
- 1+1 = 10 (carry 1)
🔟 10 Most Expected MCQs – ECET 2026 [Number Systems & Conversions]
Q1. What is the decimal equivalent of binary 1101₂?
A) 12
B) 13
C) 14
D) 15
Q2. Convert decimal 25₁₀ to binary.
A) 11001₂
B) 10100₂
C) 11101₂
D) 11010₂
Q3. What is the binary of hexadecimal A₁₆?
A) 1010
B) 1110
C) 1001
D) 1100
Q4. Convert binary 101011₂ to decimal.
A) 43
B) 44
C) 41
D) 45
Q5. Which is the base of hexadecimal number system?
A) 8
B) 10
C) 2
D) 16
Q6. What is 1A₁₆ in decimal?
A) 25
B) 26
C) 27
D) 28
Q7. Convert 45₁₀ to hexadecimal.
A) 2F
B) 2D
C) 3F
D) 2E
Q8. What is the octal equivalent of binary 111100₂?
A) 74₈
B) 76₈
C) 72₈
D) 75₈
Q9. Which of the following is NOT a valid binary number?
A) 1001
B) 11010
C) 1021
D) 111
Q10. What is the hexadecimal equivalent of binary 11011110₂?
A) DE₁₆
B) EF₁₆
C) DF₁₆
D) ED₁₆
✅ Answer Key Table
| Q.No | Answer |
|---|---|
| Q1 | B |
| Q2 | A |
| Q3 | A |
| Q4 | A |
| Q5 | D |
| Q6 | B |
| Q7 | B |
| Q8 | B |
| Q9 | C |
| Q10 | A |
🧠 Explanations of All Answers
- Q1 → B: 1101₂ = (1×8)+(1×4)+(0×2)+(1×1) = 13
- Q2 → A: 25 → 11001₂
- Q3 → A: A₁₆ = 10₁₀ = 1010₂
- Q4 → A: 101011₂ = 43₁₀
- Q5 → D: Hex uses base 16
- Q6 → B: 1A₁₆ = (1×16) + 10 = 26
- Q7 → B: 45₁₀ ÷ 16 = 2 R13 → 2D₁₆
- Q8 → B: 111100₂ = 111 100 → 7 4 → 74₈
- Q9 → C: 1021 has invalid digit 2 (not binary)
- Q10 → A: 11011110₂ → 1101 1110 = D E
🎯 Why This Practice Matters for ECET 2026
This topic is easy to learn and quick to solve in exams. Most students can score full marks if they practice well. ECET 2026 papers usually contain 1–2 direct MCQs from conversions or number system logic. Practicing these boosts speed and accuracy, especially for non-math students.
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