Digital Logic · topic
Laws and theorems with their duals, De Morgan, absorption, consensus, XOR algebra and algebraic simplification; minterms and maxterms, canonical SOP and POS, duals and complements in index form; counting Boolean, self-dual and other function classes; functional completeness by Post's five classes, NAND and NOR realisations and minimum gate counts.
The laws of two-valued Boolean algebra with their duals (identity, null, idempotent, complement, involution, distribution both ways, absorption, redundant literal, De Morgan, consensus), the duality principle and the difference between dual and complement, XOR and XNOR algebra, the missing cancellation law, a routine for algebraic simplification with five checked examples, and a verified 2026 GATE question. Every identity checked by truth table.
A partial preview of the top of the sheet. The full sheet is in the Digital Logic cheat sheet pack.
Minterms and maxterms with their index convention, canonical SOP and POS, expanding a non-canonical expression, converting between sum and product lists, complement and dual in index form, Shannon expansion in SOP and POS form, counts of all, self-dual, neutral, symmetric, 0-preserving, affine and monotone functions, how to test self-duality, and a verified 2024 GATE question.
A partial preview of the top of the sheet. The full sheet is in the Digital Logic cheat sheet pack.
Post's criterion for functional completeness with the five closed classes (0-preserving, 1-preserving, self-dual, monotone, affine), the class membership of every common gate and constant, a decision routine with verified complete and incomplete sets, two-level NAND-NAND and NOR-NOR realisation of SOP and POS, bubble pushing for active-low symbols, and minimum 2-input NAND and NOR counts found by exhaustive search.
A partial preview of the top of the sheet. The full sheet is in the Digital Logic cheat sheet pack.
