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Five basic gates: OR (Y = A+B), AND (Y = A.B), NOT (Y = A'), NAND (Y = (A.B)'), NOR (Y = (A+B)'). OR: output 1 if any input is 1. AND: output 1 only if all inputs are 1. NOT: inverts input. NAND: output 0 only if all inputs are 1 (NOT of AND). NOR: output 1 only if all inputs are 0 (NOT of OR). NAND and NOR are universal — any circuit can be built from one type alone. NOT from NAND: tie inputs together. AND from NAND: NAND followed by NAND-as-NOT. OR from NOR: NOR followed by NOR-as-NOT. De Morgan's theorems: (A.B)' = A'+B' and (A+B)' = A'.B'. These convert between AND/OR with inversions. Boolean simplification: A+AB = A, A+A'B = A+B, A(A+B) = A. JEE problems: identify output for given inputs, recognize equivalent gate combinations, simplify expressions using Boolean algebra or De Morgan's theorems.