GATE Digital Logic questions come back in a small number of shapes. For each shape: the cue in the question, the fastest method, and the lesson that teaches it.
| # | Pattern (cue) | Fastest method | Lesson |
|---|---|---|---|
| 1 | "find the base b" | write both sides as polynomials in b; keep b > every digit | Lesson 0.1.2 |
| 2 | octal ↔ hex | go through binary, regroup from the point | Lesson 0.1.2 |
| 3 | value / range of a signed pattern | 2's complement: MSB worth −2ⁿ⁻¹; ranges table | Lesson 1.1.1 |
| 4 | "does it overflow?" | same signs in, other sign out; carry into MSB ⊕ carry out | Lesson 1.1.2 |
| 5 | Booth additions/subtractions | count 10 and 01 pairs (q₋₁ = 0) | Lesson 1.1.3 |
| 6 | Gray ↔ binary, BCD, parity | g = b ⊕ (b ≫ 1); running XOR back; BCD +6 past 9 | Lesson 1.2.1 |
| 7 | IEEE hex ↔ value | S, E − 127, 1.F; group bits in 4s | Lesson 2.1.2 |
| 8 | largest / smallest float, gaps | E = 254 / 1 / denormal 2⁻¹⁴⁹; gap 2^(e − 23) | Lesson 2.1.3 |
| 9 | simplify an expression | absorption, A + A'B = A + B, consensus, De Morgan | Lesson 3.1.2 |
| 10 | Σm ↔ ΠM, number of minterms | complementary lists; k-literal term covers 2ⁿ⁻ᵏ | Lesson 3.2.1 |
| 11 | NAND/NOR counts, completeness | NOT 1, AND 2, OR 3, XOR 4 (NAND); Post's five families | Lesson 3.2.2 |
| 12 | counting functions | 2^(2ⁿ); self-dual 2^(2ⁿ⁻¹); symmetric 2ⁿ⁺¹ | Lesson 3.2.3 |
| 13 | minimal SOP / literal count | K-map: largest groups, EPIs first, skip redundant middles | Lesson 4.1.2 |
| 14 | number of PIs / EPIs | list all maximal groups; EPI = sole cover of some 1 | Lesson 4.1.2 |
| 15 | don't-cares, 5 variables | Xs only if they enlarge a group; same positions across halves | Lesson 4.1.3 |
| 16 | adder delays | RCA: (n − 1)t_c + t_s; CLA: 1 + 2 + 1 gate delays; blocks ripple 2 each | Lesson 5.1.3 |
| 17 | function of a MUX circuit | Σ (select minterm × input); 2ⁿ⁻¹:1 MUX inputs ∈ {0, 1, x, x'} | Lesson 5.2.1 |
| 18 | decoder / encoder / ROM sizes | decoder outputs are minterms; priority equations; ROM 2ⁿ × m | Lesson 5.2.2 |
| 19 | flip-flop next state, conversions | characteristic equations; excitation tables | Lesson 6.1.2 |
| 20 | maximum clock frequency | 1 / (t_pd + t_comb + t_su + skew) | Lesson 6.1.3 |
| 21 | ring / Johnson / ripple counters | n, 2n, 2ⁿ states; frequency halves per stage; mod-N clear | Lesson 6.2.2 |
| 22 | sequence of a synchronous counter | tabulate present → next for all states; check unused ones | Lesson 6.2.3 |
| 23 | FSM states and outputs | k (Mealy) / k + 1 (Moore) states; minimise by partitioning | Lesson 6.2.4 |
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Time budget in the exam
1-mark questions: under 90 seconds. 2-mark questions: under 3 minutes. Draw K-maps and counter state tables once, neatly; most wrong answers come from a cell placed in the wrong Gray-code column or a state transition misread.
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8 questions · 16 marks · 45 minutes. Negative marking on MCQ only: −1/3 mark for a wrong 1-mark MCQ, −2/3 for a wrong 2-mark MCQ. No negative marking for MSQ or NAT; MSQ has no partial credit.
Q1NAT2 marksPattern 1
In base b, 54 + 45 = 110. What is b?
Numerical answer: ________
Q2MCQ2 marksPattern 7
−0.625 in single precision (hex) is:
- (A) BF40 0000
- (B) 3F20 0000
- (C) BF20 0000
- (D) BE40 0000
Q3NAT2 marksPattern 11
Minimum number of 2-input NOR gates needed to build a 2-input OR gate?
Numerical answer: ________
Q4NAT2 marksPattern 13
F(A, B, C, D) = Σm(0, 1, 3, 7, 8, 9, 11, 15). How many literals are in the minimal SOP?
Numerical answer: ________
Q5MCQ2 marksPattern 17
F(A, B, C) = Σm(2, 3, 5, 6) is built on a 4:1 MUX with selects A (S₁) and B (S₀). The data inputs I₀ … I₃ are:
- (A) 1, 0, C', C
- (B) 0, 1, C', C
- (C) C, C', 0, 1
- (D) 0, 1, C, C'
Q6NAT2 marksPattern 20
t_pd = 4 ns, logic 11 ns, setup 3 ns, hold 1 ns. Maximum clock frequency in MHz (2 decimals)?
Numerical answer: ________
Q7NAT2 marksPattern 22
A 3-bit synchronous counter (state Q₂Q₁Q₀) uses D flip-flops with D₂ = Q₁, D₁ = Q₀, D₀ = (Q₂ + Q₁)'. Starting at 000, how many different states does it visit?
Numerical answer: ________
Q8NAT2 marksPattern 23
Minimum number of states of a Moore machine detecting the sequence 1001 (overlapping)?
Numerical answer: ________
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: 92 marks
9b + 9 = b² + b → b² − 8b − 9 = 0.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q2 Answer: (C)2 marks
−0.101₂ = −1.01 × 2⁻¹: S 1, E 126, F 01….
- (A) is wrong: That is −0.75.
- (B) is wrong: Positive.
- (D) is wrong: That is −0.1875.
Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa
Q3 Answer: 22 marks
NOR then a NOR used as NOT.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q4 Answer: 42 marks
B'C' + CD.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q5 Answer: (D)2 marks
00: 0; 01: m₂, m₃ both 1; 10: only m₅ (C = 1); 11: only m₆ (C = 0).
- (A) is wrong: Inverted.
- (B) is wrong: Last two swapped.
- (C) is wrong: Wrong rows.
Re-read: Lesson 5.2.1 — Multiplexers, and implementing functions with them
Q6 Answer: 55.55 to 55.562 marks
Period 18 ns (hold time doesn't enter the period).
Re-read: Lesson 6.1.3 — Converting flip-flops; timing and the maximum clock frequency
Q7 Answer: 52 marks
000, 001, 011, 110, 100, then 000 again.
Re-read: Lesson 6.2.3 — Synchronous counters: analysis and design
Q8 Answer: 52 marks
k + 1.
Re-read: Lesson 6.2.4 — Finite state machines: Mealy and Moore, sequence detectors, state minimisation