{"query": "Powers of two — the binary ladder", "count": 20, "results": [{"id": "card_n_a84694b9ae04", "title": "Powers of two — the binary ladder", "shelf": "science", "surface": "secular", "snippet": "The numbers a machine counts by, sealed: 2^10 = 1024 (the binary 'kilo'), 2^16 = 65,536\n(a 16-bit word's range), 2^30 = 1,073,741,824 (one GiB): https://narrowhighway.com/s/19df661045aef6fa486083cfbff"}, {"id": "card_c_1219a284fc2a", "title": "Quartz at 32,768 Hz — a power of two on the  ↔ Powers of two — the binary ladder", "shelf": "connections", "surface": null, "snippet": "run the signal through fifteen binary flip-flops, each halving the frequency, and the last ticks once per second... Time, on the wrist, is counted in powers of two.  — a concord the card itself states"}, {"id": "card_src_oeis_a002572", "title": "A002572 — Number of partitions of 1 into n powers of 1/2; or (according to one definition of \"binary\") the number of binary rooted trees.", "shelf": "oeis", "surface": "secular", "snippet": "Number of partitions of 1 into n powers of 1/2; or (according to one definition of \"binary\") the number of binary rooted trees.  First terms: 1, 1, 1, 2, 3, 5, 9, 16, 28, 50, 89, 159, 285, 510, 914, 1"}, {"id": "card_src_word_binary_system", "title": "binary system", "shelf": "dictionary", "surface": "secular", "snippet": "binary system: (noun) a positional system of numeration that uses binary digits and a radix of two — syn: binary numeration system, pure binary numeration system, binary number system"}, {"id": "card_src_word_binary_number_system", "title": "binary number system", "shelf": "dictionary", "surface": "secular", "snippet": "binary number system: (noun) a positional system of numeration that uses binary digits and a radix of two — syn: binary numeration system, pure binary numeration system, binary system"}, {"id": "card_src_word_binary_numeration_system", "title": "binary numeration system", "shelf": "dictionary", "surface": "secular", "snippet": "binary numeration system: (noun) a positional system of numeration that uses binary digits and a radix of two — syn: pure binary numeration system, binary number system, binary system"}, {"id": "card_src_word_pure_binary_numeration_system", "title": "pure binary numeration system", "shelf": "dictionary", "surface": "secular", "snippet": "pure binary numeration system: (noun) a positional system of numeration that uses binary digits and a radix of two — syn: binary numeration system, binary number system, binary system"}, {"id": "card_c_cfe6ced7e25d", "title": "Toki Pona — a whole language from 120 words ↔ Powers of two — the binary ladder", "shelf": "connections", "surface": null, "snippet": "a tiny alphabet, richly combined, spells everything — the design reality keeps choosing (DNA, binary, the elements, words)  — a concord the card itself states; mined + verified."}, {"id": "card_src_oeis_a000120", "title": "A000120 — Ones-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).", "shelf": "oeis", "surface": "secular", "snippet": "Ones-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).  First terms: 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4."}, {"id": "card_src_oeis_a000123", "title": "A000123 — Number of binary partitions: number of partitions of 2n into powers of 2.", "shelf": "oeis", "surface": "secular", "snippet": "Number of binary partitions: number of partitions of 2n into powers of 2.  First terms: 1, 2, 4, 6, 10, 14, 20, 26, 36, 46, 60, 74, 94, 114, 140, 166, 202, 238, 284, 330, 390, 450, 524, 598."}, {"id": "card_src_word_ladder_back", "title": "ladder-back", "shelf": "dictionary", "surface": "secular", "snippet": "ladder-back: (noun) a chair with a ladder-back — syn: ladder-back chair · (noun) the backrest of a chair that consists of two uprights with connecting slats"}, {"id": "card_src_word_equivalent_binary_digit_factor", "title": "equivalent-binary-digit factor", "shelf": "dictionary", "surface": "secular", "snippet": "equivalent-binary-digit factor: (noun) the average number of binary digits needed to express one radix digit in a numeration system that is not binary; on the average a number that can be expressed in"}, {"id": "card_src_word_binary", "title": "binary", "shelf": "dictionary", "surface": "secular", "snippet": "binary: (noun) a system of two stars that revolve around each other under their mutual gravitation — syn: binary star, double star · (noun) a pre-compiled, pre-linked program that is ready to run unde"}, {"id": "card_src_oeis_a000961", "title": "A000961 — Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).", "shelf": "oeis", "surface": "secular", "snippet": "Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).  First terms: 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49."}, {"id": "card_src_word_binary_operation", "title": "binary operation", "shelf": "dictionary", "surface": "secular", "snippet": "binary operation: (noun) an operation that follows the rules of Boolean algebra; each operand and the result take one of two values — syn: boolean operation, binary arithmetic operation"}, {"id": "card_src_word_binary_star", "title": "binary star", "shelf": "dictionary", "surface": "secular", "snippet": "binary star: (noun) a system of two stars that revolve around each other under their mutual gravitation — syn: binary, double star"}, {"id": "card_src_word_binary_arithmetic_operation", "title": "binary arithmetic operation", "shelf": "dictionary", "surface": "secular", "snippet": "binary arithmetic operation: (noun) an operation that follows the rules of Boolean algebra; each operand and the result take one of two values — syn: boolean operation, binary operation"}, {"id": "card_src_oeis_a003824", "title": "A003824 — Numbers that are the sum of two 4th powers in more than one way (primitive solutions).", "shelf": "oeis", "surface": "secular", "snippet": "Numbers that are the sum of two 4th powers in more than one way (primitive solutions).  First terms: 635318657, 3262811042, 8657437697, 68899596497, 86409838577, 160961094577, 2094447251857, 423152522"}, {"id": "card_src_word_binary_compound", "title": "binary compound", "shelf": "dictionary", "surface": "secular", "snippet": "binary compound: (noun) chemical compound composed of only two elements"}, {"id": "card_n_3f25971a39e2", "title": "Easton: Chronicles, Books of", "shelf": "dictionary", "surface": "secular", "snippet": "The two books were originally one. They bore the title in the Massoretic Hebrew Dibre hayyamim, i.e., “Acts of the Days.” This title was rendered by Jerome in his Latin version “Chronicon,” and hence "}]}