3431:
of the digit 1. Any terminating expansion in the ternary system is equivalent to the expression that is identical up to the term preceding the last non-zero term followed by the term one less than the last non-zero term of the first expression, followed by an infinite tail of twos. For example: 0.1020 is equivalent to 0.1012222... because the expansions are the same until the "two" of the first expression, the two was decremented in the second expansion, and trailing zeros were replaced with trailing twos in the second expression.
3339:
3430:
conveniently. Additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have a ternary expression that does not contain any instance
3482:
Simulation of ternary computers using binary computers, or interfacing between ternary and binary computers, can involve use of binary-coded ternary (BCT) numbers, with two or three bits used to encode each trit. BCT encoding is analogous to
3342:
Use of ternary numbers to balance an unknown integer weight from 1 to 40 kg with weights of 1, 3, 9 and 27 kg (4 ternary digits actually gives 3 = 81 possible combinations: −40 to +40, but only the positive values are
3920:
3580:
3487:(BCD) encoding. If the trit values 0, 1 and 2 are encoded 00, 01 and 10, conversion in either direction between binary-coded ternary and binary can be done in
3419:(which is sometimes used as an alternative by some record keepers). In this usage, only the fractional part of the number is written in ternary form.
3787:
3374:
reference at all. Where the signal is usually grounded to a certain reference, or at a certain voltage level, the state is said to be high
4115:
723:
3665:"Hybrid signed–digit number systems: a unified framework for redundant number representations with bounded carry propagation chains"
4486:
4120:
443:
3947:
4110:
4105:
3763:
4093:
3994:
3891:
3846:
4542:
3470:, is sometimes used in low-level software and hardware to accomplish fast addition of integers because it can eliminate
3709:
Frieder, Gideon; Luk, Clement (February 1975). "Algorithms for Binary Coded
Balanced and Ordinary Ternary Operations".
276:
4271:
3397:. For example, if a player pitched all of the 4th, 5th and 6th innings, plus achieving 2 outs in the 7th inning, his
3455:. It has been used for some computing systems because of this efficiency. It is also used to represent three-option
4244:
3463:
3352:
67:
3318:(base 27, each digit is three ternary digits) can be used for compact representation of ternary, similar to how
4361:
4166:
4098:
4060:
3711:
3672:
915:(six digits). However, they are still far less compact than the corresponding representations in bases such as
510:
17:
716:
291:
3746:
Parhami, Behrooz; McKeown, Michael (2013-11-03). "Arithmetic with binary-encoded balanced ternary numbers".
3378:
because it is open and serves its own reference. Thus, the actual voltage level is sometimes unpredictable.
3347:
In certain analog logic, the state of the circuit is often expressed ternary. This is most commonly seen in
4537:
4261:
4191:
4039:
636:
4516:
4151:
3467:
463:
646:
4547:
4139:
2325:
in decimal); but a major drawback is that, in turn, ternary does not offer a finite representation for
523:
4449:
4401:
4313:
4291:
4286:
4214:
4080:
3450:
3443:
619:
388:
3686:
4323:
3987:
3604:
3492:
825:
most often refers to a system in which the three digits are all non–negative numbers; specifically
709:
36:
3488:
4476:
4391:
3887:
699:
483:
80:
3961:
344:
4219:
4075:
3681:
299:
3423:
4209:
4184:
3447:
3439:
3327:
862:
501:
4011:
3967:
3838:
3484:
3375:
3360:
3356:
928:
815:
596:
457:
450:
331:
3644:
Soltanifar, Mohsen (2006). "A Different
Description of A Family of Middle–α Cantor Sets".
8:
4481:
4459:
4386:
4239:
4231:
3980:
3664:
678:
668:
543:
494:
306:
238:
93:
54:
3581:"A complete beginner's guide to baseball stats: Pitching statistics, and what they mean"
2416:) is not representable exactly (that would need e.g. decimal); nor is one-sixth (senary
2321:
as same as senary (as opposed to its cumbersome representation as an infinite string of
133:
4464:
4444:
4396:
4371:
4156:
4125:
3899:
3817:
3781:
3769:
3728:
3471:
3389:), to denote fractional parts of an inning. Since the team on offense is allowed three
591:
181:
176:
123:
128:
4351:
4281:
4256:
4070:
4065:
3944:
3842:
3759:
2322:
673:
663:
651:
631:
586:
581:
517:
349:
321:
228:
161:
151:
138:
103:
98:
3732:
3370:). In this configuration the output of the circuit is actually not connected to any
566:
4496:
4381:
4179:
3912:
3802:
3773:
3751:
3720:
3691:
3547:
3504:
846:
838:
808:
742:
576:
470:
223:
211:
156:
146:
113:
88:
3956:
3863:
4501:
4366:
4318:
4251:
3951:
3832:
3398:
3315:
2302:
920:
792:
688:
658:
601:
571:
556:
316:
284:
256:
233:
216:
75:
3338:
171:
4454:
4276:
4266:
4174:
3755:
3390:
3364:
919:– see below for a compact way to codify ternary using nonary (base 9) and
858:
768:
683:
626:
606:
561:
434:
166:
118:
44:
4531:
4376:
3552:
3523:
3435:
3381:
A rare "ternary point" in common use is for defensive statistics in
American
2381:
489:
378:
311:
251:
186:
108:
3724:
4333:
4308:
3393:, each out is considered one third of a defensive inning and is denoted as
2378:
869:
641:
4511:
4506:
4356:
4303:
4130:
3916:
3558:
3323:
611:
476:
428:
418:
4416:
4411:
4328:
4296:
4201:
4144:
3459:, such as phone menu systems, which allow a simple path to any branch.
3427:
3422:
Ternary numbers can be used to convey self-similar structures like the
2374:
834:
830:
826:
780:
413:
3862:
Brousentsov, N. P.; Maslov, S. P.; Ramil
Alvarez, J.; Zhogolev, E. A.
3695:
4491:
4469:
4426:
4421:
4088:
4044:
4003:
423:
3837:. First IFIP WG 9.7 Conference, SoRuCom 2006. Petrozavodsk, Russia:
2954:
4406:
3908:
3382:
3861:
3304:(3, 3) = 3 − 1 = 26 = 2 × 3 + 2 × 3 + 2 × 3 = 18 + 6 + 2
3386:
3371:
916:
866:
408:
393:
3309:
3625:
Soltanifar, Mohsen (2006). "On A sequence of cantor
Fractals".
3538:
876:
842:
398:
757:
3972:
3964: – includes fractional part, from Maths Is Fun
3864:"Development of ternary computers at Moscow State University"
3543:
3508:
3319:
861:
in ternary do not get uncomfortably lengthy as quickly as in
784:
403:
365:
326:
751:
4024:
3526:
3348:
760:
3748:
2013 Asilomar
Conference on Signals, Systems and Computers
4019:
3516:
902:
788:
3466:
called a binary signed-digit number system, a form of
3750:. Pacific Grove, California, US. pp. 1130–1133.
3314:
Nonary (base 9, each digit is two ternary digits) or
754:
3830:
748:
3968:
Gideon
Frieder's replacement ternary numeral system
745:
2990:digits, all of which are the maximal digit value
2955:Sum of the digits in ternary as opposed to binary
2384:of the base; as with base two, one-tenth (decimal
4529:
3957:The ternary calculating machine of Thomas Fowler
3855:
3824:
3637:
3618:
3578:
2305:, ternary offers a convenient way to represent
3745:
3988:
3831:Impagliazzo, John; Proydakov, Eduard (2006).
3627:Rose Hulman Undergraduate Mathematics Journal
3310:Compact ternary representation: base 9 and 27
717:
3911:, the Scientific Research Society: 490–494.
3834:Perspectives on Soviet and Russian Computing
3434:Ternary is the integer base with the lowest
3148: − ... − b − 1
852:
3809:
3794:
3739:
3702:
3662:
1456:Numbers from 0 to 3 − 1 in standard ternary
837:, the adjective also lends its name to the
3995:
3981:
3786:: CS1 maint: location missing publisher (
3708:
3656:
3646:American Journal of Undergraduate Research
3643:
3624:
724:
710:
3685:
845:, 0 and +1, used in comparison logic and
3495:supporting BCT arithmetic is available.
3401:column for that game would be listed as
3337:
3477:
3359:. The output is said to either be low (
14:
4530:
3818:"Ternary Data Types for C Programmers"
3803:"Binary Coded Ternary and its Inverse"
3446:. This is due to its proximity to the
3976:
3886:
3815:
3800:
3515:to be six trits or approximately 9.5
3519:(holding more information than the
24:
3880:
3333:
3299:For a three-digit ternary number,
2959:The value of a binary number with
25:
4559:
3938:
3663:Phatak, D. S.; Koren, I. (1994).
3816:Jones, Douglas W. (2015-12-29).
814: 3 (about 1.58496) bits of
741:
3926:from the original on 2019-10-30
3801:Jones, Douglas W. (June 2016).
3579:Ashley MacLennan (2019-01-09).
3464:redundant binary representation
4002:
3712:IEEE Transactions on Computers
3673:IEEE Transactions on Computers
3597:
3572:
841:system; comprising the digits
13:
1:
4061:Arbitrary-precision or bignum
3607:. MLB (Major League Baseball)
3565:
3326:systems are used in place of
807:). One trit is equivalent to
2887:
2831:
2763:
2692:
2459:
2266:
2231:
2186:
2123:
2063:
2029:
2009:
1989:
1959:
1929:
1880:
1848:
1771:
1739:
1703:
1671:
1629:
1597:
1561:
1529:
1492:
1460:
7:
3532:
3468:signed-digit representation
3353:transistor–transistor logic
10:
4564:
4543:Positional numeral systems
4034:
3890:(November–December 2001).
3756:10.1109/ACSSC.2013.6810470
2060:
1736:
1594:
444:Non-standard radices/bases
4435:
4402:Strongly typed identifier
4344:
4230:
4200:
4165:
4053:
4010:
3605:"Stats - Team - Pitching"
853:Comparison to other bases
3498:
2970:Similarly, for a number
4477:Parametric polymorphism
3962:Ternary Base Conversion
3725:10.1109/T-C.1975.224188
2963:bits that are all 1 is
700:List of numeral systems
3438:, followed closely by
3351:circuits, and also in
3344:
1925:Powers of 3 in ternary
888:corresponds to binary
3448:mathematical constant
3341:
68:Hindu–Arabic numerals
27:Base-3 numeral system
3917:10.1511/2001.40.3268
3485:binary-coded decimal
3478:Binary-coded ternary
3405:, the equivalent of
2455:Fractions in ternary
929:multiplication table
597:Prehistoric counting
373:Common radices/bases
55:Place-value notation
4538:Computer arithmetic
4482:Primitive data type
4387:Recursive data type
4240:Algebraic data type
4116:Quadruple precision
3424:Sierpinski triangle
2457:
1927:
1458:
931:
857:Representations of
544:Sign-value notation
4445:Abstract data type
4126:Extended precision
4085:Reduced precision
3950:2011-05-14 at the
3945:Ternary Arithmetic
3900:American Scientist
3385:(usually just for
3363:), high, or open (
3345:
2453:
1923:
1454:
926:
200:East Asian systems
4548:Ternary computers
4525:
4524:
4257:Associative array
4121:Octuple precision
3765:978-1-4799-2390-8
3696:10.1109/12.295850
3505:ternary computers
3357:totem-pole output
2950:
2949:
2373:, etc.), because
2297:
2296:
1913:
1912:
1450:
1449:
905:) and to ternary
847:ternary computers
787:. Analogous to a
734:
733:
533:
532:
16:(Redirected from
4555:
4497:Type constructor
4382:Opaque data type
4314:Record or Struct
4111:Double precision
4106:Single precision
3997:
3990:
3983:
3974:
3973:
3934:
3932:
3931:
3925:
3896:
3874:
3873:
3871:
3870:
3859:
3853:
3852:
3848:978-3-64222816-2
3828:
3822:
3821:
3813:
3807:
3806:
3798:
3792:
3791:
3785:
3777:
3743:
3737:
3736:
3706:
3700:
3699:
3689:
3669:
3660:
3654:
3653:
3641:
3635:
3634:
3622:
3616:
3615:
3613:
3612:
3601:
3595:
3594:
3592:
3591:
3576:
3548:ternary computer
3489:logarithmic time
3418:
3417:
3413:
3410:
3305:
3295:
3289:
3272:
3270:
3268:
3267:
3261:
3258:
3253: − 1)(
3243:
3226:
3197:
3195:
3193:
3192:
3186:
3183:
3166:
3149:
3131:
3107:
3098:
3081:
3068: − 1)(
3063:
3046:
2997:, we can write:
2996:
2966:
2946:
2940:
2934:
2925:
2916:
2910:
2898:
2884:
2875:
2869:
2857:
2848:
2828:
2822:
2816:
2810:
2804:
2795:
2789:
2783:
2774:
2760:
2754:
2748:
2742:
2733:
2727:
2721:
2715:
2709:
2700:
2688:
2686:
2685:
2682:
2679:
2669:
2667:
2666:
2663:
2660:
2650:
2648:
2647:
2644:
2641:
2631:
2629:
2628:
2625:
2622:
2612:
2610:
2609:
2606:
2603:
2593:
2591:
2590:
2587:
2584:
2574:
2572:
2571:
2568:
2565:
2555:
2553:
2552:
2549:
2546:
2536:
2534:
2533:
2530:
2527:
2517:
2515:
2514:
2511:
2508:
2498:
2496:
2495:
2492:
2489:
2479:
2477:
2476:
2473:
2470:
2458:
2452:
2447:
2445:
2444:
2441:
2438:
2431:
2429:
2428:
2425:
2422:
2415:
2413:
2412:
2409:
2406:
2399:
2397:
2396:
2393:
2390:
2372:
2370:
2369:
2366:
2363:
2356:
2354:
2353:
2350:
2347:
2340:
2338:
2337:
2334:
2331:
2323:recurring digits
2320:
2318:
2317:
2314:
2311:
2303:rational numbers
2293:
2288:
2283:
2278:
2273:
2263:
2262:
2255:
2254:
2247:
2246:
2228:
2227:
2220:
2219:
2212:
2211:
2204:
2203:
2196:
2195:
2183:
2182:
2179:
2176:
2169:
2168:
2165:
2162:
2155:
2154:
2151:
2144:
2143:
2140:
2133:
2132:
2120:
2119:
2116:
2113:
2106:
2105:
2102:
2095:
2094:
2091:
2084:
2083:
2080:
2073:
2072:
2056:
2051:
2046:
2041:
2036:
1986:
1985:
1978:
1977:
1956:
1955:
1948:
1947:
1928:
1922:
1845:
1844:
1837:
1836:
1829:
1828:
1821:
1820:
1813:
1812:
1805:
1804:
1797:
1796:
1789:
1788:
1781:
1780:
1668:
1667:
1660:
1659:
1526:
1525:
1459:
1453:
1446:
1445:
1438:
1437:
1430:
1429:
1422:
1421:
1414:
1413:
1406:
1405:
1398:
1397:
1377:
1376:
1369:
1368:
1361:
1360:
1353:
1352:
1345:
1344:
1337:
1336:
1313:
1312:
1305:
1304:
1297:
1296:
1289:
1288:
1281:
1280:
1273:
1272:
1249:
1248:
1241:
1240:
1233:
1232:
1225:
1224:
1217:
1216:
1190:
1189:
1182:
1181:
1174:
1173:
1166:
1165:
1136:
1135:
1128:
1127:
1120:
1119:
1087:
1086:
932:
925:
923:(base 27).
911:
910:
897:
896:
893:
884:
883:
839:balanced ternary
767:
766:
763:
762:
759:
756:
753:
750:
747:
726:
719:
712:
515:
499:
481:
471:balanced ternary
468:
455:
61:
60:
32:
31:
21:
4563:
4562:
4558:
4557:
4556:
4554:
4553:
4552:
4528:
4527:
4526:
4521:
4502:Type conversion
4437:
4431:
4367:Enumerated type
4340:
4226:
4220:null-terminated
4196:
4161:
4049:
4006:
4001:
3952:Wayback Machine
3941:
3929:
3927:
3923:
3894:
3883:
3881:Further reading
3878:
3877:
3868:
3866:
3860:
3856:
3849:
3829:
3825:
3814:
3810:
3799:
3795:
3779:
3778:
3766:
3744:
3740:
3707:
3703:
3687:10.1.1.352.6407
3667:
3661:
3657:
3642:
3638:
3623:
3619:
3610:
3608:
3603:
3602:
3598:
3589:
3587:
3577:
3573:
3568:
3535:
3501:
3491:. A library of
3480:
3415:
3411:
3408:
3406:
3399:innings pitched
3336:
3334:Practical usage
3316:septemvigesimal
3312:
3300:
3294: − 1.
3276:
3275:
3262:
3259:
3257: − 1)
3248:
3247:
3245:
3230:
3229:
3221: − 1)
3205:
3187:
3184:
3178:
3177:
3175:
3170:
3153:
3135:
3111:
3103: − 1)
3085:
3084:
3050:
3049:
3041: − 1)
3033: − 1)
3025: − 1)
3017: − 1)
3001:
2991:
2965:2 − 1
2964:
2957:
2944:
2938:
2932:
2923:
2914:
2908:
2896:
2882:
2873:
2867:
2855:
2846:
2826:
2820:
2814:
2808:
2802:
2793:
2787:
2781:
2772:
2758:
2752:
2746:
2740:
2731:
2725:
2719:
2713:
2707:
2698:
2683:
2680:
2677:
2676:
2674:
2664:
2661:
2658:
2657:
2655:
2645:
2642:
2639:
2638:
2636:
2626:
2623:
2620:
2619:
2617:
2607:
2604:
2601:
2600:
2598:
2588:
2585:
2582:
2581:
2579:
2569:
2566:
2563:
2562:
2560:
2550:
2547:
2544:
2543:
2541:
2531:
2528:
2525:
2524:
2522:
2512:
2509:
2506:
2505:
2503:
2493:
2490:
2487:
2486:
2484:
2474:
2471:
2468:
2467:
2465:
2442:
2439:
2436:
2435:
2433:
2426:
2423:
2420:
2419:
2417:
2410:
2407:
2404:
2403:
2401:
2394:
2391:
2388:
2387:
2385:
2367:
2364:
2361:
2360:
2358:
2351:
2348:
2345:
2344:
2342:
2335:
2332:
2329:
2328:
2326:
2315:
2312:
2309:
2308:
2306:
2291:
2286:
2281:
2276:
2271:
2260:
2258:
2252:
2250:
2244:
2242:
2225:
2223:
2217:
2215:
2209:
2207:
2201:
2199:
2193:
2191:
2180:
2177:
2174:
2172:
2166:
2163:
2160:
2158:
2152:
2149:
2147:
2141:
2138:
2136:
2130:
2128:
2117:
2114:
2111:
2109:
2103:
2100:
2098:
2092:
2089:
2087:
2081:
2078:
2076:
2070:
2068:
2054:
2049:
2044:
2039:
2034:
1983:
1981:
1975:
1973:
1953:
1951:
1945:
1943:
1842:
1840:
1834:
1832:
1826:
1824:
1818:
1816:
1810:
1808:
1802:
1800:
1794:
1792:
1786:
1784:
1778:
1776:
1665:
1663:
1657:
1655:
1523:
1521:
1443:
1441:
1435:
1433:
1427:
1425:
1419:
1417:
1411:
1409:
1403:
1401:
1395:
1393:
1374:
1372:
1366:
1364:
1358:
1356:
1350:
1348:
1342:
1340:
1334:
1332:
1310:
1308:
1302:
1300:
1294:
1292:
1286:
1284:
1278:
1276:
1270:
1268:
1246:
1244:
1238:
1236:
1230:
1228:
1222:
1220:
1214:
1212:
1187:
1185:
1179:
1177:
1171:
1169:
1163:
1161:
1133:
1131:
1125:
1123:
1117:
1115:
1084:
1082:
921:septemvigesimal
914:
908:
906:
900:
894:
891:
889:
887:
881:
879:
874:
865:. For example,
859:integer numbers
855:
812:
744:
740:
730:
694:
693:
616:
602:Proto-cuneiform
547:
546:
535:
534:
529:
528:
513:
497:
479:
466:
453:
440:
369:
368:
356:
355:
336:
296:
281:
272:
271:
262:
261:
243:
202:
201:
192:
191:
143:
85:
71:
70:
58:
57:
45:Numeral systems
28:
23:
22:
15:
12:
11:
5:
4561:
4551:
4550:
4545:
4540:
4523:
4522:
4520:
4519:
4514:
4509:
4504:
4499:
4494:
4489:
4484:
4479:
4474:
4473:
4472:
4462:
4457:
4455:Data structure
4452:
4447:
4441:
4439:
4433:
4432:
4430:
4429:
4424:
4419:
4414:
4409:
4404:
4399:
4394:
4389:
4384:
4379:
4374:
4369:
4364:
4359:
4354:
4348:
4346:
4342:
4341:
4339:
4338:
4337:
4336:
4326:
4321:
4316:
4311:
4306:
4301:
4300:
4299:
4289:
4284:
4279:
4274:
4269:
4264:
4259:
4254:
4249:
4248:
4247:
4236:
4234:
4228:
4227:
4225:
4224:
4223:
4222:
4212:
4206:
4204:
4198:
4197:
4195:
4194:
4189:
4188:
4187:
4182:
4171:
4169:
4163:
4162:
4160:
4159:
4154:
4149:
4148:
4147:
4137:
4136:
4135:
4134:
4133:
4123:
4118:
4113:
4108:
4103:
4102:
4101:
4096:
4094:Half precision
4091:
4081:Floating point
4078:
4073:
4068:
4063:
4057:
4055:
4051:
4050:
4048:
4047:
4042:
4037:
4032:
4027:
4022:
4016:
4014:
4008:
4007:
4000:
3999:
3992:
3985:
3977:
3971:
3970:
3965:
3959:
3954:
3940:
3939:External links
3937:
3936:
3935:
3882:
3879:
3876:
3875:
3854:
3847:
3823:
3808:
3793:
3764:
3738:
3719:(2): 212–215.
3701:
3680:(8): 880–891.
3655:
3636:
3617:
3596:
3585:Bless You Boys
3570:
3569:
3567:
3564:
3563:
3562:
3555:
3550:
3541:
3534:
3531:
3500:
3497:
3479:
3476:
3335:
3332:
3311:
3308:
3297:
3296:
3273:
3266: − 1
3227:
3199:
3198:
3191: − 1
3182: − 1
3168:
3165: − 1
3151:
3133:
3109:
3082:
3047:
2995: − 1
2956:
2953:
2952:
2951:
2948:
2947:
2941:
2935:
2929:
2926:
2920:
2917:
2911:
2905:
2902:
2899:
2893:
2890:
2886:
2885:
2879:
2876:
2870:
2864:
2861:
2858:
2852:
2849:
2843:
2840:
2837:
2834:
2830:
2829:
2823:
2817:
2811:
2805:
2799:
2796:
2790:
2784:
2778:
2775:
2769:
2766:
2762:
2761:
2755:
2749:
2743:
2737:
2734:
2728:
2722:
2716:
2710:
2704:
2701:
2695:
2691:
2690:
2671:
2652:
2633:
2614:
2595:
2576:
2557:
2538:
2519:
2500:
2481:
2462:
2299:
2298:
2295:
2294:
2289:
2284:
2279:
2274:
2269:
2265:
2264:
2256:
2248:
2240:
2237:
2234:
2230:
2229:
2221:
2213:
2205:
2197:
2189:
2185:
2184:
2170:
2156:
2145:
2134:
2126:
2122:
2121:
2107:
2096:
2085:
2074:
2066:
2062:
2061:
2058:
2057:
2052:
2047:
2042:
2037:
2032:
2028:
2027:
2024:
2021:
2018:
2015:
2012:
2008:
2007:
2004:
2001:
1998:
1995:
1992:
1988:
1987:
1979:
1971:
1968:
1965:
1962:
1958:
1957:
1949:
1941:
1938:
1935:
1932:
1919:
1918:
1915:
1914:
1911:
1910:
1907:
1904:
1901:
1898:
1895:
1892:
1889:
1886:
1883:
1879:
1878:
1875:
1872:
1869:
1866:
1863:
1860:
1857:
1854:
1851:
1847:
1846:
1838:
1830:
1822:
1814:
1806:
1798:
1790:
1782:
1774:
1770:
1769:
1766:
1763:
1760:
1757:
1754:
1751:
1748:
1745:
1742:
1738:
1737:
1734:
1733:
1730:
1727:
1724:
1721:
1718:
1715:
1712:
1709:
1706:
1702:
1701:
1698:
1695:
1692:
1689:
1686:
1683:
1680:
1677:
1674:
1670:
1669:
1661:
1653:
1650:
1647:
1644:
1641:
1638:
1635:
1632:
1628:
1627:
1624:
1621:
1618:
1615:
1612:
1609:
1606:
1603:
1600:
1596:
1595:
1592:
1591:
1588:
1585:
1582:
1579:
1576:
1573:
1570:
1567:
1564:
1560:
1559:
1556:
1553:
1550:
1547:
1544:
1541:
1538:
1535:
1532:
1528:
1527:
1519:
1516:
1513:
1510:
1507:
1504:
1501:
1498:
1495:
1491:
1490:
1487:
1484:
1481:
1478:
1475:
1472:
1469:
1466:
1463:
1448:
1447:
1439:
1431:
1423:
1415:
1407:
1399:
1391:
1388:
1385:
1379:
1378:
1370:
1362:
1354:
1346:
1338:
1330:
1327:
1324:
1321:
1315:
1314:
1306:
1298:
1290:
1282:
1274:
1266:
1263:
1260:
1257:
1251:
1250:
1242:
1234:
1226:
1218:
1210:
1207:
1204:
1201:
1198:
1192:
1191:
1183:
1175:
1167:
1159:
1156:
1153:
1150:
1147:
1144:
1138:
1137:
1129:
1121:
1113:
1110:
1107:
1104:
1101:
1098:
1095:
1089:
1088:
1080:
1077:
1074:
1071:
1068:
1065:
1062:
1059:
1056:
1050:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1016:
1015:
1012:
1009:
1006:
1003:
1000:
997:
994:
991:
988:
982:
981:
976:
971:
966:
961:
956:
951:
946:
941:
936:
912:
898:
885:
872:
854:
851:
810:
769:numeral system
732:
731:
729:
728:
721:
714:
706:
703:
702:
696:
695:
692:
691:
686:
681:
676:
671:
666:
661:
656:
655:
654:
649:
644:
634:
629:
623:
622:
615:
614:
609:
604:
599:
594:
589:
584:
579:
574:
569:
564:
559:
553:
552:
551:Non-alphabetic
548:
542:
541:
540:
537:
536:
531:
530:
527:
526:
521:
508:
492:
487:
474:
461:
447:
446:
439:
438:
431:
426:
421:
416:
411:
406:
401:
396:
391:
386:
381:
375:
374:
370:
363:
362:
361:
358:
357:
354:
353:
347:
341:
340:
335:
334:
329:
324:
319:
314:
309:
303:
302:
300:Post-classical
295:
294:
288:
287:
280:
279:
273:
269:
268:
267:
264:
263:
260:
259:
254:
248:
247:
242:
241:
236:
231:
226:
221:
220:
219:
208:
207:
203:
199:
198:
197:
194:
193:
190:
189:
184:
179:
174:
169:
164:
159:
154:
149:
142:
141:
136:
131:
126:
121:
116:
111:
106:
101:
96:
91:
84:
83:
81:Eastern Arabic
78:
76:Western Arabic
72:
66:
65:
64:
59:
53:
52:
51:
48:
47:
41:
40:
26:
18:Ternary number
9:
6:
4:
3:
2:
4560:
4549:
4546:
4544:
4541:
4539:
4536:
4535:
4533:
4518:
4515:
4513:
4510:
4508:
4505:
4503:
4500:
4498:
4495:
4493:
4490:
4488:
4485:
4483:
4480:
4478:
4475:
4471:
4468:
4467:
4466:
4463:
4461:
4458:
4456:
4453:
4451:
4448:
4446:
4443:
4442:
4440:
4434:
4428:
4425:
4423:
4420:
4418:
4415:
4413:
4410:
4408:
4405:
4403:
4400:
4398:
4395:
4393:
4390:
4388:
4385:
4383:
4380:
4378:
4377:Function type
4375:
4373:
4370:
4368:
4365:
4363:
4360:
4358:
4355:
4353:
4350:
4349:
4347:
4343:
4335:
4332:
4331:
4330:
4327:
4325:
4322:
4320:
4317:
4315:
4312:
4310:
4307:
4305:
4302:
4298:
4295:
4294:
4293:
4290:
4288:
4285:
4283:
4280:
4278:
4275:
4273:
4270:
4268:
4265:
4263:
4260:
4258:
4255:
4253:
4250:
4246:
4243:
4242:
4241:
4238:
4237:
4235:
4233:
4229:
4221:
4218:
4217:
4216:
4213:
4211:
4208:
4207:
4205:
4203:
4199:
4193:
4190:
4186:
4183:
4181:
4178:
4177:
4176:
4173:
4172:
4170:
4168:
4164:
4158:
4155:
4153:
4150:
4146:
4143:
4142:
4141:
4138:
4132:
4129:
4128:
4127:
4124:
4122:
4119:
4117:
4114:
4112:
4109:
4107:
4104:
4100:
4097:
4095:
4092:
4090:
4087:
4086:
4084:
4083:
4082:
4079:
4077:
4074:
4072:
4069:
4067:
4064:
4062:
4059:
4058:
4056:
4052:
4046:
4043:
4041:
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4021:
4018:
4017:
4015:
4013:
4012:Uninterpreted
4009:
4005:
3998:
3993:
3991:
3986:
3984:
3979:
3978:
3975:
3969:
3966:
3963:
3960:
3958:
3955:
3953:
3949:
3946:
3943:
3942:
3922:
3918:
3914:
3910:
3906:
3902:
3901:
3893:
3889:
3885:
3884:
3865:
3858:
3850:
3844:
3840:
3836:
3835:
3827:
3819:
3812:
3804:
3797:
3789:
3783:
3775:
3771:
3767:
3761:
3757:
3753:
3749:
3742:
3734:
3730:
3726:
3722:
3718:
3714:
3713:
3705:
3697:
3693:
3688:
3683:
3679:
3675:
3674:
3666:
3659:
3651:
3647:
3640:
3633:(1). Paper 9.
3632:
3628:
3621:
3606:
3600:
3586:
3582:
3575:
3571:
3561:
3560:
3556:
3554:
3553:Ternary logic
3551:
3549:
3545:
3542:
3540:
3537:
3536:
3530:
3528:
3525:
3522:
3518:
3514:
3510:
3506:
3496:
3494:
3490:
3486:
3475:
3473:
3469:
3465:
3460:
3458:
3454:
3453:
3449:
3445:
3441:
3437:
3436:radix economy
3432:
3429:
3425:
3420:
3404:
3400:
3396:
3392:
3388:
3384:
3379:
3377:
3373:
3369:
3368:
3362:
3358:
3354:
3350:
3340:
3331:
3329:
3325:
3321:
3317:
3307:
3303:
3293:
3287:
3283:
3279:
3274:
3265:
3256:
3252:
3241:
3237:
3233:
3228:
3224:
3220:
3216:
3212:
3208:
3204:
3203:
3202:
3190:
3181:
3173:
3169:
3164:
3160:
3157: −
3156:
3152:
3147:
3144: −
3143:
3139:
3134:
3130:
3126:
3122:
3118:
3114:
3110:
3106:
3102:
3096:
3092:
3088:
3083:
3079:
3075:
3071:
3067:
3061:
3057:
3053:
3048:
3044:
3040:
3036:
3032:
3028:
3024:
3020:
3016:
3012:
3008:
3004:
3000:
2999:
2998:
2994:
2989:
2985:
2981:
2977:
2973:
2968:
2962:
2942:
2936:
2930:
2927:
2921:
2918:
2912:
2906:
2903:
2900:
2894:
2891:
2888:
2880:
2877:
2871:
2865:
2862:
2859:
2853:
2850:
2844:
2841:
2838:
2835:
2832:
2824:
2818:
2812:
2806:
2800:
2797:
2791:
2785:
2779:
2776:
2770:
2767:
2764:
2756:
2750:
2744:
2738:
2735:
2729:
2723:
2717:
2711:
2705:
2702:
2696:
2693:
2689:
2672:
2670:
2653:
2651:
2634:
2632:
2615:
2613:
2596:
2594:
2577:
2575:
2558:
2556:
2539:
2537:
2520:
2518:
2501:
2499:
2482:
2480:
2463:
2460:
2456:
2451:
2450:
2449:
2383:
2380:
2376:
2324:
2304:
2290:
2285:
2280:
2275:
2270:
2267:
2257:
2249:
2241:
2238:
2235:
2232:
2222:
2214:
2206:
2198:
2190:
2187:
2171:
2157:
2146:
2135:
2127:
2124:
2108:
2097:
2086:
2075:
2067:
2064:
2059:
2053:
2048:
2043:
2038:
2033:
2030:
2025:
2022:
2019:
2016:
2013:
2010:
2005:
2002:
1999:
1996:
1993:
1990:
1980:
1972:
1969:
1966:
1963:
1960:
1950:
1942:
1939:
1936:
1933:
1930:
1926:
1921:
1920:
1917:
1916:
1908:
1905:
1902:
1899:
1896:
1893:
1890:
1887:
1884:
1881:
1876:
1873:
1870:
1867:
1864:
1861:
1858:
1855:
1852:
1849:
1839:
1831:
1823:
1815:
1807:
1799:
1791:
1783:
1775:
1772:
1767:
1764:
1761:
1758:
1755:
1752:
1749:
1746:
1743:
1740:
1735:
1731:
1728:
1725:
1722:
1719:
1716:
1713:
1710:
1707:
1704:
1699:
1696:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1662:
1654:
1651:
1648:
1645:
1642:
1639:
1636:
1633:
1630:
1625:
1622:
1619:
1616:
1613:
1610:
1607:
1604:
1601:
1598:
1593:
1589:
1586:
1583:
1580:
1577:
1574:
1571:
1568:
1565:
1562:
1557:
1554:
1551:
1548:
1545:
1542:
1539:
1536:
1533:
1530:
1520:
1517:
1514:
1511:
1508:
1505:
1502:
1499:
1496:
1493:
1488:
1485:
1482:
1479:
1476:
1473:
1470:
1467:
1464:
1461:
1457:
1452:
1451:
1440:
1432:
1424:
1416:
1408:
1400:
1392:
1389:
1386:
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1328:
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1264:
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771:(also called
770:
765:
739:
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713:
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707:
705:
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637:Alphasyllabic
635:
633:
630:
628:
625:
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308:
305:
304:
301:
298:
297:
293:
290:
289:
286:
283:
282:
278:
275:
274:
270:Other systems
266:
265:
258:
255:
253:
252:Counting rods
250:
249:
245:
244:
240:
237:
235:
232:
230:
227:
225:
222:
218:
215:
214:
213:
210:
209:
205:
204:
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195:
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185:
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180:
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173:
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97:
95:
92:
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79:
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50:
49:
46:
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4282:Intersection
4029:
3928:. Retrieved
3904:
3898:
3892:"Third base"
3888:Hayes, Brian
3867:. Retrieved
3857:
3833:
3826:
3811:
3796:
3747:
3741:
3716:
3710:
3704:
3677:
3671:
3658:
3649:
3645:
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3630:
3626:
3620:
3609:. Retrieved
3599:
3588:. Retrieved
3584:
3574:
3557:
3520:
3512:
3507:such as the
3502:
3481:
3461:
3456:
3451:
3433:
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3402:
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3366:
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2983:
2982:) with base
2979:
2975:
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2969:
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2883:024340531215
2827:000100111011
2673:
2654:
2635:
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973:
968:
963:
958:
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948:
943:
938:
856:
822:
820:
804:
800:
796:
791:, a ternary
776:
772:
737:
735:
503:
464:Signed-digit
383:
339:Contemporary
206:Contemporary
29:
4512:Type theory
4507:Type system
4357:Bottom type
4304:Option type
4245:generalized
4131:Long double
4076:Fixed point
3559:Taixuanjing
3324:hexadecimal
816:information
642:Akṣarapallī
612:Tally marks
511:Non-integer
4532:Categories
4417:Empty type
4412:Type class
4362:Collection
4319:Refinement
4297:metaobject
4145:signedness
4004:Data types
3930:2020-04-12
3869:2010-01-20
3652:(2): 9–12.
3611:2020-07-30
3590:2020-07-30
3566:References
3511:defined a
3462:A form of
3444:quaternary
3428:Cantor set
2874:0313452421
2815:0001011101
2432:, decimal
927:A ternary
679:Glagolitic
652:Kaṭapayādi
620:Alphabetic
524:Asymmetric
366:radix/base
307:Cistercian
292:Babylonian
239:Vietnamese
94:Devanagari
4492:Subtyping
4487:Interface
4470:metaclass
4422:Unit type
4392:Semaphore
4372:Exception
4277:Inductive
4267:Dependent
4232:Composite
4210:Character
4192:Reference
4089:Minifloat
4045:Bit array
3782:cite book
3682:CiteSeerX
3376:impedance
2461:Fraction
2400:, senary
2377:is not a
2341:(nor for
821:Although
647:Āryabhaṭa
592:Kharosthi
484:factorial
451:Bijective
352:(Iñupiaq)
182:Sundanese
177:Mongolian
124:Malayalam
4517:Variable
4407:Top type
4272:Equality
4180:physical
4157:Rational
4152:Interval
4099:bfloat16
3948:Archived
3921:Archived
3909:Sigma Xi
3839:Springer
3733:38704739
3533:See also
3521:de facto
3387:pitchers
3383:baseball
3361:grounded
2889:Decimal
2694:Ternary
2233:Decimal
2065:Ternary
2011:Decimal
1931:Ternary
1882:Decimal
1741:Ternary
1705:Decimal
1599:Ternary
1563:Decimal
1462:Ternary
803:nary dig
674:Georgian
664:Cyrillic
632:Armenian
587:Etruscan
582:Egyptian
490:Negative
350:Kaktovik
345:Cherokee
322:Pentadic
246:Historic
229:Japanese
162:Javanese
152:Balinese
139:Dzongkha
104:Gurmukhi
99:Gujarati
37:a series
35:Part of
4460:Generic
4436:Related
4352:Boolean
4309:Product
4185:virtual
4175:Address
4167:Pointer
4140:Integer
4071:Decimal
4066:Complex
4054:Numeric
3774:9603084
3472:carries
3426:or the
3414:⁄
3372:voltage
3343:useful)
3269:
3246:
3194:
3176:
3029:+ … + (
2833:Senary
2765:Binary
2687:
2675:
2668:
2656:
2649:
2637:
2630:
2618:
2611:
2599:
2592:
2580:
2573:
2561:
2554:
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2497:
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2478:
2466:
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2430:
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2386:
2371:
2359:
2355:
2343:
2339:
2327:
2319:
2307:
2301:As for
2188:Senary
2125:Binary
1991:Senary
1961:Binary
1850:Senary
1773:Binary
1673:Senary
1631:Binary
1531:Senary
1494:Binary
917:decimal
867:decimal
823:ternary
783:as its
777:trinary
738:ternary
577:Chuvash
495:Complex
285:Ancient
277:History
224:Hokkien
212:Chinese
157:Burmese
147:Tibetan
134:Kannada
114:Sinhala
89:Bengali
4450:Boxing
4438:topics
4397:Stream
4334:tagged
4292:Object
4215:String
3845:
3772:
3762:
3731:
3684:
3539:Qutrit
3524:binary
3493:C code
3440:binary
3328:binary
3123:+ … +
3076:+ … +
2945:076923
2919:0.125
2915:142857
2803:000111
2726:010212
2382:factor
2268:Power
2031:Power
901:(nine
877:senary
863:binary
833:, and
779:) has
773:base 3
689:Hebrew
659:Coptic
572:Brahmi
557:Aegean
514:
498:
480:
467:
454:
317:Muisca
257:Tangut
234:Korean
217:Suzhou
129:Telugu
4345:Other
4329:Union
4262:Class
4252:Array
4035:Tryte
3924:(PDF)
3907:(6).
3895:(PDF)
3770:S2CID
3729:S2CID
3668:(PDF)
3544:Setun
3513:tryte
3509:Setun
3503:Some
3499:Tryte
3457:trees
3365:high-
3355:with
3320:octal
3217:) = (
3201:Then
3080:+ 1),
3013:) = (
2860:0.043
2798:0.001
2747:00211
2379:prime
1652:1111
795:is a
793:digit
781:three
684:Greek
669:Geʽez
627:Abjad
607:Roman
567:Aztec
562:Attic
477:Mixed
435:table
327:Quipu
312:Mayan
167:Khmer
119:Tamil
4465:Kind
4427:Void
4287:List
4202:Text
4040:Word
4030:Trit
4025:Byte
3843:ISBN
3788:link
3760:ISBN
3717:C-24
3546:, a
3527:byte
3517:bits
3442:and
3391:outs
3349:CMOS
3322:and
3167:, or
3150:, so
2986:and
2937:0.08
2901:0.25
2878:0.03
2863:0.04
2842:0.13
2819:0.00
2809:0011
2782:0011
2777:0.01
2741:0022
2736:0.01
2714:0121
2181:0011
2178:1110
2175:1100
2167:0001
2164:1010
2161:1001
2153:1011
2150:1000
2148:1000
2142:1001
2139:1101
2131:0011
2129:1111
2006:213
1984:0001
1976:1011
1970:1001
1843:1010
1835:1001
1827:1000
1819:0111
1811:0110
1803:0101
1795:0100
1787:0011
1779:0010
1768:222
1666:0001
1658:0000
1649:1110
1646:1101
1643:1100
1640:1011
1637:1010
1634:1001
1626:122
1048:200
1014:100
903:bits
895:1101
892:0110
873:(10)
797:trit
785:base
332:Rumi
187:Thai
109:Odia
4324:Set
4020:Bit
3913:doi
3752:doi
3721:doi
3692:doi
3529:).
3403:3.2
3140:= −
3132:and
3099:= (
3064:= (
3037:+ (
3021:+ (
2928:0.1
2907:0.1
2904:0.2
2892:0.5
2866:0.0
2851:0.1
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2836:0.3
2807:0.0
2794:001
2786:0.0
2768:0.1
2759:002
2751:0.0
2718:0.0
2703:0.1
2448:).
2261:683
2253:561
2245:187
2239:729
2236:243
2226:043
2224:231
2218:213
2210:043
2202:213
2194:043
2173:100
2118:000
2115:000
2112:000
2104:000
2101:000
2099:100
2093:000
2090:000
2082:000
2079:000
2071:000
2069:100
2026:81
1982:101
1954:000
1946:000
1940:100
1909:26
1877:42
1765:221
1762:220
1759:212
1756:211
1753:210
1750:202
1747:201
1744:200
1732:17
1700:25
1623:121
1620:120
1617:112
1614:111
1611:110
1608:102
1605:101
1602:100
1558:12
1524:000
1518:111
1515:110
1512:101
1509:100
1489:22
1444:000
1436:200
1428:100
1420:000
1412:200
1404:100
1396:000
1390:200
1387:100
1383:100
1375:200
1367:101
1359:002
1351:210
1343:111
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1329:220
1326:121
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1295:211
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1223:100
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1206:200
1203:110
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1180:111
1172:022
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1155:202
1152:120
1149:101
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1103:110
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913:(3)
909:112
907:111
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886:(6)
882:405
875:or
870:365
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801:tri
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775:or
752:ɜːr
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172:Lao
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3780:{{
3768:.
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3727:.
3715:.
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3678:43
3676:.
3670:.
3648:.
3629:.
3583:.
3474:.
3395:.1
3330:.
3306:.
3290:=
3284:,
3244:=
3238:,
3213:,
3174:=
3161:=
3155:bM
3127:+
3119:+
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3113:bM
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2137:10
2088:10
2023:27
2003:43
2000:13
1967:11
1952:10
1937:10
1906:25
1903:24
1900:23
1897:22
1894:21
1891:20
1888:19
1885:18
1874:41
1871:40
1868:35
1865:34
1862:33
1859:32
1856:31
1853:30
1729:16
1726:15
1723:14
1720:13
1717:12
1714:11
1711:10
1697:24
1694:23
1691:22
1688:21
1685:20
1682:15
1679:14
1676:13
1590:8
1555:11
1552:10
1506:11
1503:10
1486:21
1483:20
1480:12
1477:11
1474:10
1442:10
1323:22
1319:22
1259:21
1255:21
1200:20
1196:20
1146:12
1142:12
1100:22
1097:11
1093:11
1061:20
1058:10
1054:10
1033:22
1030:20
1027:11
1011:22
1008:21
1005:20
1002:12
999:11
996:10
974:22
969:21
964:20
959:12
954:11
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849:.
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818:.
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758:ər
736:A
429:60
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419:16
414:12
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3872:.
3851:.
3820:.
3805:.
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3776:.
3754::
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3723::
3698:.
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3650:5
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3593:.
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3416:3
3412:2
3409:+
3407:3
3367:Z
3302:N
3292:b
3288:)
3286:d
3282:b
3280:(
3278:N
3271:,
3264:b
3260:/
3255:b
3251:b
3249:(
3242:)
3240:d
3236:b
3234:(
3232:N
3225:,
3223:M
3219:b
3215:d
3211:b
3209:(
3207:N
3196:.
3189:b
3185:/
3180:b
3172:M
3163:b
3159:M
3146:b
3142:b
3138:M
3136:−
3129:b
3125:b
3121:b
3117:b
3108:.
3105:M
3101:b
3097:)
3095:d
3091:b
3089:(
3087:N
3078:b
3074:b
3070:b
3066:b
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3060:d
3056:b
3054:(
3052:N
3045:,
3043:b
3039:b
3035:b
3031:b
3027:b
3023:b
3019:b
3015:b
3011:d
3007:b
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3003:N
2993:b
2988:d
2984:b
2980:d
2976:b
2974:(
2972:N
2961:n
2939:3
2924:1
2909:6
2897:3
2868:3
2847:1
2720:1
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2678:1
2662:/
2659:1
2643:/
2640:1
2624:/
2621:1
2608:9
2605:/
2602:1
2589:8
2586:/
2583:1
2570:7
2567:/
2564:1
2551:6
2548:/
2545:1
2532:5
2529:/
2526:1
2513:4
2510:/
2507:1
2494:3
2491:/
2488:1
2475:2
2472:/
2469:1
2443:6
2440:/
2437:1
2424:/
2421:1
2408:/
2405:1
2392:/
2389:1
2375:2
2368:8
2365:/
2362:1
2352:4
2349:/
2346:1
2336:2
2333:/
2330:1
2316:3
2313:/
2310:1
2292:3
2287:3
2282:3
2277:3
2272:3
2251:6
2243:2
2200:3
2192:1
2159:1
2110:1
2077:1
2055:3
2050:3
2045:3
2040:3
2035:3
2020:9
2017:3
2014:1
1997:3
1994:1
1974:1
1964:1
1944:1
1934:1
1841:1
1833:1
1825:1
1817:1
1809:1
1801:1
1793:1
1785:1
1777:1
1708:9
1664:1
1656:1
1587:7
1584:6
1581:5
1578:4
1575:3
1572:2
1569:1
1566:0
1549:5
1546:4
1543:3
1540:2
1537:1
1534:0
1522:1
1500:1
1497:0
1471:2
1468:1
1465:0
1434:2
1426:2
1418:2
1410:1
1402:1
1394:1
1373:2
1365:2
1357:2
1349:1
1341:1
1333:1
1309:2
1301:2
1293:1
1285:1
1277:1
1269:1
1245:2
1237:1
1229:1
1221:1
1213:1
1186:1
1178:1
1170:1
1162:1
1132:1
1124:1
1116:1
1083:1
1024:2
1020:2
993:2
990:1
986:1
944:2
939:1
935:×
890:1
880:1
835:2
831:1
827:0
811:2
799:(
764:/
761:i
755:n
749:t
746:ˈ
743:/
725:e
718:t
711:v
520:)
518:φ
516:(
507:)
504:i
502:2
500:(
486:)
482:(
473:)
469:(
460:)
458:1
456:(
437:)
433:(
404:8
399:6
394:5
389:4
384:3
379:2
20:)
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