{"id": "card_cs_logic_gates", "kind": "reference", "title": "Logic gates — the 16 functions of two inputs", "body": "Of two inputs there are exactly 2^(2^2) = 16 Boolean functions (sealed) - AND, OR, XOR, NAND and the rest; NAND alone builds them all. From gates come adders, memory and processors. All computation is wired from this finite logic. The algebra the gates are functions in is George Boole's - An Investigation of the Laws of Thought (1854), two values and one law of their own, x*x = x, which Boole named the fundamental law of thought (the law of duality). Rests on the instruments (formal logic) and on Boole.", "source": {"label": "Narrow Highway — computer science", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "computer_science", "bands": ["computer science", "pillar", "logic_gates", "one map"], "subject": "Logic gates — the 16 functions of two inputs", "connections": [{"to_card_id": "card_floor_computer_science", "relationship": "part_of", "evidence": "a pillar of computer science (Logic gates)"}, {"to_card_id": "card_floor_the_instruments", "relationship": "connects_at", "evidence": "Boolean logic is the formal-logic instrument - gates from truth functions"}, {"to_card_id": "card_src_book_15114", "relationship": "connects_at", "evidence": "Boole 1854 - the two-valued algebra the gates are functions in; x*x = x, the law of duality"}, {"to_card_id": "card_theory_boolean_algebra_propositional_logic", "relationship": "connects_at", "evidence": "Boolean algebra / propositional logic - the theory card of the same algebra"}, {"to_card_id": "card_cs_sorting_algorithms", "relationship": "connects_at", "evidence": "a comparison is one Boolean decision; the three-way comparison (<, =, >) is the third value, -1 0 1"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.computer.science", "facets": {"subject": ["computer science", "logic_gates", "one map", "pillar"]}, "presentation": {"glyph": "•", "kind_label": "computer science", "by": "Narrow Highway — computer science", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_computer_science", "title": "Computer science — bits, logic, and what can be computed", "relationship": "part of", "why": "a pillar of computer science (Logic gates)", "href": "/card/card_floor_computer_science", "resolved": true}, {"id": "card_floor_the_instruments", "title": "The instruments — every verifier and validator, and where they join", "relationship": "connects at", "why": "Boolean logic is the formal-logic instrument - gates from truth functions", "href": "/card/card_floor_the_instruments", "resolved": true}, {"id": "card_src_book_15114", "title": "An Investigation of the Laws of Thought On which are founded the mathematical theories of logic and probabilities — George Boole", "relationship": "connects at", "why": "Boole 1854 - the two-valued algebra the gates are functions in; x*x = x, the law of duality", "href": "/card/card_src_book_15114", "resolved": true}, {"id": "card_theory_boolean_algebra_propositional_logic", "title": "Boolean algebra / propositional logic", "relationship": "connects at", "why": "Boolean algebra / propositional logic - the theory card of the same algebra", "href": "/card/card_theory_boolean_algebra_propositional_logic", "resolved": true}, {"id": "card_cs_sorting_algorithms", "title": "Sorting algorithms — the roll of eighty-six and the bound none can beat", "relationship": "connects at", "why": "a comparison is one Boolean decision; the three-way comparison (<, =, >) is the third value, -1 0 1", "href": "/card/card_cs_sorting_algorithms", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_cs_logic_gates", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_cs_logic_gates"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}