ACompressed recap
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Gates: AND (all), OR (any), NOT, NAND, NOR, XOR (odd number of 1s), XNOR. n variables → 2ⁿ rows. Laws: absorption A + AB = A, A + A'B = A + B, A + BC = (A + B)(A + C), De Morgan, consensus AB + A'C + BC = AB + A'C. Dual: swap + ↔ ·, 0 ↔ 1. Complement: swap and complement literals.
BMerged rule card
3.1.1 Logic gates and truth tables
- AND: 1 iff all 1. OR: 1 iff any 1. NOT inverts. NAND = (AND)', NOR = (OR)'.
- XOR: 1 iff an odd number of inputs are 1; XNOR is its NOT.
- n variables → 2ⁿ truth-table rows, numbered by the input bits (first variable = MSB).
- Precedence: NOT, then AND, then OR.
3.1.2 Boolean algebra: laws, duality, De Morgan and algebraic simplification
- Identity, null, idempotent, complement, involution, commutative, associative.
- Distributive both ways: A(B + C) = AB + AC and A + BC = (A + B)(A + C).
- Absorption A + AB = A; redundant literal A + A'B = A + B; consensus AB + A'C + BC = AB + A'C.
- De Morgan (A + B)' = A'B', (AB)' = A' + B'. Complement: swap operators and complement literals.
- Dual: swap + ↔ · and 0 ↔ 1 only. XOR: A ⊕ B = A'B + AB'.
CInterleaved GATE-style questions
Q1NAT1 markXOR
A 5-input XOR gate has inputs 1, 1, 0, 1, 1. What is its output?
Numerical answer: ________
Q2MCQ1 markNOR
For inputs A = 0, B = 0, which gate outputs 0?
- (A) OR
- (B) NAND
- (C) NOR
- (D) XNOR
Q3NAT2 marksTruth table
F(A, B, C) = A'B + AC. How many rows make F = 1?
Numerical answer: ________
Q4MCQ1 markDistributive
Which identity is true in Boolean algebra?
- (A) A(B + C) = AB + C
- (B) A + B = AB
- (C) (AB)' = A'B'
- (D) A + BC = (A + B)(A + C)
Q5MCQ2 marksConsensus
AB + A'C + BC is equivalent to:
- (A) B + C
- (B) A'C + BC
- (C) AB + A'C
- (D) AB + BC
Q6MCQ1 markDe Morgan
(A + B + C)' equals:
- (A) A'BC
- (B) A'B'C'
- (C) A' + B' + C'
- (D) (ABC)'
Q7MCQ1 markXOR identity
A ⊕ 1 equals:
- (A) 0
- (B) 1
- (C) A'
- (D) A
Q8MCQ2 marksSimplify
A(A' + B) + B(B + C) simplifies to:
- (A) B
- (B) A + B
- (C) B + C
- (D) AB
DAnswer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: 01 mark
Four 1s: even.
Re-read: Lesson 3.1.1 — Logic gates and truth tables
Q2 Answer: (A)1 mark
OR of two 0s is 0.
- (B) is wrong: 1.
- (C) is wrong: 1.
- (D) is wrong: Equal inputs → 1.
Re-read: Lesson 3.1.1 — Logic gates and truth tables
Q3 Answer: 42 marks
Rows 2, 3, 5, 7.
Re-read: Lesson 3.1.1 — Logic gates and truth tables
Q4 Answer: (D)1 mark
The "extra" distributive law.
- (A) is wrong: C should be AC.
- (B) is wrong: False for 01.
- (C) is wrong: That is not De Morgan; (AB)' = A' + B'.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q5 Answer: (C)2 marks
BC is the consensus term.
- (A) is wrong: Too big (row 010).
- (B) is wrong: Loses AB (row 110).
- (D) is wrong: Loses A'C (row 001).
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q6 Answer: (B)1 mark
NOT of OR is AND of NOTs.
- (A) is wrong: No.
- (C) is wrong: That is (ABC)'.
- (D) is wrong: Same as B.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q7 Answer: (C)1 mark
XOR with 1 inverts.
- (A) is wrong: That is A ⊕ A.
- (B) is wrong: No.
- (D) is wrong: That is A ⊕ 0.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q8 Answer: (A)2 marks
AB + B + BC = B (absorption).
- (B) is wrong: Too big.
- (C) is wrong: Too big.
- (D) is wrong: Too small.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification