Logic Gates & Boolean Algebra — A/L Physics

What must I remember about Logic Gates & Boolean Algebra?

• Binary Logic States: Logic 1 (HIGH, typically +5 V in TTL logic) and Logic 0 (LOW, typically 0 V / Ground).
• Fundamental Logic Gates: NOT (Inverter: Y = Ā); AND (Conjunction: Y = A · B, output 1 only when all inputs 1); OR (Disjunction: Y = A + B, output 1 when at least one input 1).
• Universal Logic Gates: NAND (Y = (A · B)̄) and NOR (Y = (A + B)̄); called universal because ANY Boolean logic function, circuit, or flip-flop can be synthesized using NAND gates alone or NOR gates alone.
• Boolean Algebra Theorems: Commutative, Associative, and Distributive Laws (A · (B + C) = A·B + A·C; A + (B · C) = (A + B)(A + C)); De Morgan's Laws: (A + B)̄ = Ā · B̄ and (A · B)̄ = Ā + B̄.

Test yourself (1 minute)

1. Exclusive-OR (XOR) & XNOR Gates

   XOR: Y = A ⊕ B = Ā B + A B̄ (output 1 when inputs are DIFFERENT; used in binary adders and parity checkers); XNOR: Y = A ⊙ B = A B + Ā B̄ (output 1 when inputs are IDENTICAL).

2. Synthesis of NOT from NAND

   Tie both inputs of a 2-input NAND gate together: Y = (A · A)̄ = Ā.

3. Redundancy / Absorption Rules in Boolean Algebra

   A + A·B = A; A + Ā·B = A + B; A · (A + B) = A; A · (Ā + B) = A · B.

Practise Logic Gates & Boolean Algebra questions today

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 9: Electronics

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Where does Logic Gates & Boolean Algebra fit in the syllabus?

Unit 9.7 · Year 2 · Term 2