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FE · 8% of the exam

Digital Systems practice questions

10 free Digital Systems questions for the FE Electrical and Computer Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questionsFree 10-question FE quiz

What this domain covers

Logic design from number systems to sequential circuits: Boolean algebra, gates, Karnaugh maps, flip-flops and state machines.

Exam weight
8%
On a real exam
≈ 9 questions
In our bank
48 questions

Topics that come up most

  • Number systems and conversions
  • Boolean algebra and logic gates
  • Karnaugh map minimisation
  • Flip-flops and timing diagrams
  • State machines and sequential circuits

How to study it

Practise K-map minimisation and flip-flop timing diagrams with a pencil; both reward a careful, step-by-step method.

Sample Digital Systems questions

Try each one before opening the answer. Original questions written to the official exam objectives.

  1. Question 1

    On a Karnaugh map, adjacent cells differ in:

    • AEvery variable
    • BExactly one variable
    • CNo variables
    • DExactly two variables
    Show answer and explanation

    Answer: B) Exactly one variable

    • AIncorrect. They differ in one.
    • BCorrect. That's why grouping simplifies expressions.
    • CIncorrect. Each cell is a different combination.
    • DIncorrect. They differ in one.

  2. Question 2

    An 8-to-3 priority encoder outputs:

    • AThe binary code of the highest-priority active input
    • BEight outputs from three inputs
    • CThe sum of all inputs
    • DA single parity bit
    Show answer and explanation

    Answer: A) The binary code of the highest-priority active input

    • ACorrect. It compresses 8 lines into 3 bits.
    • BIncorrect. That's a decoder.
    • CIncorrect. That isn't an encoder.
    • DIncorrect. That isn't an encoder.

  3. Question 3

    Hexadecimal 3C in binary is:

    • A0011 1100
    • B0011 0011
    • C1100 0011
    • D0011 1010
    Show answer and explanation

    Answer: A) 0011 1100

    • ACorrect. Each hex digit is four bits.
    • BIncorrect. That's 33.
    • CIncorrect. That's C3.
    • DIncorrect. That's 3A.

  4. Question 4

    NAND gates are called universal because they can:

    • AReplace all wiring
    • BStore data indefinitely
    • CRun at any clock speed
    • DImplement any Boolean function
    Show answer and explanation

    Answer: D) Implement any Boolean function

    • AIncorrect. They can implement any function.
    • BIncorrect. That's memory.
    • CIncorrect. They can implement any function.
    • DCorrect. NOR gates are universal too.

  5. Question 5

    In a synchronous circuit, flip-flops have a clock-to-Q delay of 2 ns, a setup time of 1 ns, and a hold time of 0.5 ns. The slowest combinational path between two flip-flops has a delay of 6 ns. Ignoring clock skew, what is the approximate maximum clock frequency?

    • A105 MHz
    • B111 MHz
    • C143 MHz
    • D167 MHz
    Show answer and explanation

    Answer: B) 111 MHz

    The clock period must cover the clock-to-Q delay, the critical-path logic delay and the setup time: T_min = 2 + 6 + 1 = 9 ns, so f_max ≈ 111 MHz. Hold time does not affect the maximum frequency.

    • AIncorrect. This adds the hold time to the period (9.5 ns). Hold time limits minimum path delay, not the clock period.
    • BCorrect. The minimum period is 2 + 6 + 1 = 9 ns, so f_max = 1/9 ns ≈ 111 MHz.
    • CIncorrect. This uses 7 ns (logic delay plus setup) and leaves out the 2 ns clock-to-Q delay.
    • DIncorrect. This uses only the 6 ns logic delay and leaves out the clock-to-Q delay and the setup time.

  6. Question 6

    The minimum number of bits needed to represent 100 distinct values is:

    • A100
    • B6
    • C10
    • D7
    Show answer and explanation

    Answer: D) 7

    • AIncorrect. Use \(\log_2\).
    • BIncorrect. \(2^6 = 64\) is too few.
    • CIncorrect. 7 bits suffice.
    • DCorrect. \(2^7 = 128 \ge 100\).

  7. Question 7

    Shifting a binary number one place to the left, filling with 0, is equivalent to:

    • ANegating the number
    • BDividing by 2
    • CAdding 1
    • DMultiplying by 2
    Show answer and explanation

    Answer: D) Multiplying by 2

    • AIncorrect. That isn't the effect.
    • BIncorrect. That's a right shift.
    • CIncorrect. That isn't the effect.
    • DCorrect. Shifting right divides by 2.

  8. Question 8

    A function of 3 Boolean variables has how many possible minterms?

    • A8
    • B3
    • C6
    • D9
    Show answer and explanation

    Answer: A) 8

    • ACorrect. A function of n variables has \(2^n = 2^3\) minterms.
    • BIncorrect. That's the number of variables.
    • CIncorrect. Use \(2^n\).
    • DIncorrect. Use \(2^n\).

  9. Question 9

    An XOR gate with one input tied to a control signal C acts as a:

    • AControlled inverter
    • BConstant 0 output
    • CConstant 1 output
    • DMemory cell
    Show answer and explanation

    Answer: A) Controlled inverter

    • ACorrect. When C = 0 it passes the input.
    • BIncorrect. It passes or inverts the input.
    • CIncorrect. It passes or inverts the input.
    • DIncorrect. It's combinational.

  10. Question 10

    Decimal 25 in binary is:

    • A10011
    • B10101
    • C11100
    • D11001
    Show answer and explanation

    Answer: D) 11001

    • AIncorrect. That's 19.
    • BIncorrect. That's 21.
    • CIncorrect. That's 28.
    • DCorrect. 16 + 8 + 1.

Digital Systems: FAQs

How much of the FE exam is Digital Systems?

Digital Systems is 8% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 9 questions. The real exam's exact split varies by form.

What does the Digital Systems domain cover?

Logic design from number systems to sequential circuits: Boolean algebra, gates, Karnaugh maps, flip-flops and state machines.

How should I study Digital Systems for FE?

Practise K-map minimisation and flip-flop timing diagrams with a pencil; both reward a careful, step-by-step method.

Where can I practise more Digital Systems questions?

This page has 10 free Digital Systems questions with answers. The ExamWize FE question bank has 48 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Other FE topics

Also: 15 free questions across all topics, the FE cheat sheet and the study guide.

Get Digital Systems exam-ready

The full FE bank has 48 Digital Systems questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

See the full FE practice examsTake the free diagnostic

Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.