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Digital electronics: board exam questions with solutions

On the ECE exam under Electronics Engineering. Try each question before you open its solution, then practise with fresh numbers below: 2 computed question types on this topic.

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Build it in the lab

NAND gate · NAND as a universal gate · D flip-flop · JK flip-flop · 4-bit ripple counter: the same circuits on a live bench, with meters you can move.

Questions

1. Which pair consists of universal gates, each able to implement any Boolean function on its own?

  1. AND and OR
  2. NAND and NOR
  3. XOR and XNOR
  4. AND and NOT
Show the answer and solution

Answer: B. NAND and NOR

NAND alone (or NOR alone) can build NOT, AND and OR, so either is functionally complete.

2. What is the decimal value of the unsigned binary number 10110110?

  1. 182
  2. 174
  3. 186
  4. 118
Show the answer and solution

Answer: A. 182

128 + 32 + 16 + 4 + 2 = 182 (hex B6).

3. What decimal value does the 8-bit two's-complement number 11101100 represent?

  1. 236
  2. −108
  3. −19
  4. −20
Show the answer and solution

Answer: D. −20

MSB is 1, so it is negative: invert to 00010011 and add 1 → 00010100 = 20, so the value is −20.

4. Simplify the Boolean expression AB + AB′ + A′B.

  1. AB
  2. A ⊕ B
  3. A + B
  4. A + B′
Show the answer and solution

Answer: C. A + B

AB + AB′ = A; then A + A′B = A + B.

5. What is the minimum number of flip-flops needed to build a MOD-12 counter?

  1. 3
  2. 4
  3. 6
  4. 12
Show the answer and solution

Answer: B. 4

n flip-flops give 2ⁿ states; 2³ = 8 < 12 ≤ 16 = 2⁴, so 4 flip-flops are needed.

6. A 1 MHz clock drives a 3-bit asynchronous (ripple) binary counter. What is the frequency at the most significant bit output?

  1. 125 kHz
  2. 333 kHz
  3. 250 kHz
  4. 500 kHz
Show the answer and solution

Answer: A. 125 kHz

Each stage divides by 2: 1 MHz / 2³ = 125 kHz.

7. What is the minimal sum-of-products form of F(A, B, C) = Σm(0, 2, 4, 5, 6)?

  1. A′ + C′
  2. C′ + A′B
  3. B′C′ + AC
  4. C′ + AB′
Show the answer and solution

Answer: D. C′ + AB′

On the K-map, minterms 0, 2, 4, 6 form a quad giving C′; minterms 4 and 5 pair to give AB′. So F = C′ + AB′.

8. By De Morgan's theorem, (A + B)′ equals which expression?

  1. A′ + B′
  2. AB
  3. A′B′
  4. (AB)′
Show the answer and solution

Answer: C. A′B′

De Morgan: the complement of a sum is the product of the complements, (A + B)′ = A′·B′.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. What is the least number of flip-flops needed for a mod-410 counter?

  1. 9
  2. 52
  3. 10
  4. 8
Show the answer and solution

Answer: A. 9

n flip-flops count 2ⁿ states; 2^8 = 256 < 410 ≤ 2^9 = 512, so 9.

10. A 4 MHz clock drives a 4-stage binary ripple counter. What is the frequency at the last output?

  1. 250 kHz
  2. 500 kHz
  3. 64 MHz
  4. 1 MHz
Show the answer and solution

Answer: A. 250 kHz

Each toggle flip-flop halves the frequency: 4 MHz/2^4 = 250 kHz.

Other topics in the same subjects

DC circuits · AC circuits · Transients (RC, RL, RLC) · Semiconductors and diodes · BJT and FET circuits · Operational amplifiers · Oscillators and feedback · Power electronics · Microprocessors and microcontrollers · Control systems · Instrumentation and measurement

An independent, free reviewer: not affiliated with the PRC or the Boards. Subject weights and passing rules are from the PRC examination programs and the laws (RA 9292, RA 7920); check the current PRC program before you file. Code questions follow the Philippine Electrical Code 2017 Part 1; check them against your own copy of the Code.