# AAT ICAS 2041 ✧ NC calculation factors

this document describes AAT ICAS calculation factors for the New Calendar system. please refer to AAT ICAS 2040 for additional important information about calculation factor guidelines.

- new calendar calculation factors
- table 2041.1 ✧ some New Calendar formula resources
- table 2041.2 ✧ New Calendar Day Notation day factors

## New Calendar calculation factors

a number of general and specific methods for formatting and factoring dates and times are described in a variety of other resources including operating system documentation, application documentation, UNIX manual pages, APIs for Java and other languages, ISO 8601, and so forth.

developers and users should consider any scale factors among the New Calendar scale, the New Calendar Day Notation scale, and other scales of years and days. the use of a particular method of calculation or factoring may involve the following considerations: the particular scale that a time, day, or year is derived from; the relationships among particular scale factors; the particular fixed or coordinated implementation of a particular scale to dates in the far past or far future; and whether the designation or observance of a particular date is based on a particular scale.

- factor a UCA- or AD-era year to an NC-era year by adding 10 000. likewise factor a UCA- or AD-era NC year to a UCA or an AD year by subtracting 10 000.
- factor a BC-era year* to NC by subtracting from 10 001. also factor a BC-era NC year to a BC year* by subtracting from 10 001 (*subject to BC-year conformance with New Calendar year).

to calculate a New Calendar Day Notation date from a UCN date for years in a positive scale:

- take the year component of the date (is equivalent to number of prior whole years from beginning of scale to the year of the particular day to be specified) A.
- multiply year component A by 365 days for intermediate number of days B.
- divide year component A by 4 and take integer value for intermediate number of leap years C.
- divide year component A by 100 and take integer value for century year adjustment D.
- divide year component A by 400 and take integer value for century leap year adjustment E.
- apply year zero leap adjustment Z: if year component A is greater than or equal to 1, then Z = 1, otherwise Z = 0.
- (determine any further leap year adjustments to reflect correct methods of year and day counting)
- determine number of particular leap days F = C - D + E + Z.
- determine day number of the last day of the last prior whole year G = B + F.
- determine day-of-year number of the day to be counted H.
- determine NDN day notation number J = H + G.

UCN 12000A01 at IDC t500 deka(0) corresponds to NDN 4382911.5 and to JD 2451545 and provides a calculation factor of 1 931 366.5 days between the NDN and JD scales.

Macintosh computer serial dating day 0 at UCN 11904A01 corresponds to NDN 4347847 and to AD 1904 January 01, and provides a calculation factor of 4 347 847 days between the NDN and Macintosh serial dating scales (based on UT time for both scales).

Windows computer serial dating day 1 at UCN 11900A01 corresponds to NDN 4346387 and to AD 1900 January 01, and provides a calculation factor of 4 346 386 days between the NDN and Windows serial dating scales (based on UT time for both scales).

table 2041.1 ✧ some New Calendar formula resources

resource | formula |
---|---|

resource | formula |

for any NC-era year yNC, for any Gregorian-era year yG (AD 1582 or later per Gregorian calendar), for any Julian* BC-era year yBC (*subject to yBC conformance with New Calendar year), for any Julian Day day JD, for any New Calendar Day Notation day NDN, for any Macintosh computer serial date dateMac (based on UT for all scales), for any Windows computer serial date dateWin (based on UT for all scales): | |

4 and 100 year rule | IF (yNC/4) = INTEGER(yNC/4) AND IF (yNC/100) does NOT EQUAL integer of (yNC/100), THEN yNC is a leap year. |

400 year rule | IF (yNC/400) = INTEGER(yNC/400), THEN year is a leap year. |

year zero rule | IF yNC = zero, THEN yNC is a leap year. |

leap year rule | IF either the 4 and 100 year rule, the 400 year rule, OR the year zero rules is TRUE, THEN a yNC is a leap year. |

G to NC calculation | yNC = yG + 10 000. |

G to NC correspondence | NC 12000 corresponds to AD 2000. |

UCA to NC calculation | yNC = yUCA + 10 000. |

NC to UCA calculation | yUCA = yNC - 10 000. |

NC to BC calculation | yNC = 10 001 - yBC. |

BC to NC calculation | yBC = 10 001 -yNC. |

JD to NDN calculation | NDN = JD + 1 931 366.5. |

MJD to NDN calculation | NDN = MJD + 4331367. |

NDN to JD calculation | JD = NDN - 1 931 366.5. |

NDN to MJD calculation | MJD = NDN - 4331367. |

dateMac to NDN calculation | NDN = dateMac + 4 347 847. |

dateWin to NDN calculation | NDN = dateWin + 4 346 386. |

special note: ensure that numerical expressions are represented to an appropriate number of places, even if the beginning places are leading zeroes. |

table 2041.2 ✧ New Calendar Day Notation day factors

UCN date | NDN date |
---|---|

UCN date | NDN date |

UCN 00000A01 | NDN 001 |

UCN 00000M36 | NDN 366 |

UCN 00001N01 | NDN 367 |

UCN 00001Z35 | NDN 731 |

UCN 00002A01 | NDN 732 |

UCN 00002M35 | NDN 1096 |

UCN 00003N01 | NDN 1097 |

UCN 00003Z35 | NDN 1461 |

UCN 00004A01 | NDN 1462 |

UCN 00004M36 | NDN 1827 |

UCN 00005N01 | NDN 1828 |

UCN 00005Z35 | NDN 2192 |

UCN 00006N01 | NDN 2193 |

UCN 00006Z35 | NDN 2557 |

UCN 00007N01 | NDN 2558 |

UCN 00007Z35 | NDN 2922 |

UCN 00008A01 | NDN 2923 |

UCN 00008M36 | NDN 3288 |

UCN 00009N01 | NDN 3289 |

UCN 00009Z35 | NDN 3653 |

UCN 5287Y28 IDC t500 deka(0) | NDN 1931366.5 (JD 1 or BC 4713 January 01) |

UCN 11582K17 | NDN 4230526 (Julian calendar date 1582 October 04 Thursday) |

UCN 11582K18 | NDN 4230527 (Gregorian calendar date 1582 October 15 Friday) |

UCN 11800M35 | NDN 4310227 |

UCN 11858L21 | NDN 4331367 (t000 is MJD day 0 or JD 2400000.5) |

UCN 11900A01 | NDN 4346387 (day 1 of Windows serial dating) |

UCN 11900M35 | NDN 4346751 |

UCN 11904A01 | NDN 4347847 (day 0 of Macintosh serial dating) |

UCN 11909Z35 | NDN 4350038 |

UCN 11919Z35 | NDN 4353690 |

UCN 11929Z35 | NDN 4357343 |

UCN 11939Z35 | NDN 4360995 |

UCN 11949Z35 | NDN 4364648 |

UCN 11959Z35 | NDN 4368300 |

UCN 11969Z35 | NDN 4371953 |

UCN 11979Z35 | NDN 4375605 |

UCN 11989Z35 | NDN 4379258 |

UCN 11999Z35 | NDN 4382910 |

UCN 12000M36 | NDN 4383276 |

UCN 12001Z35 | NDN 4383641 |

UCN 12002M35 | NDN 4384006 |

UCN 12003Z35 | NDN 4384371 |

UCN 12004M36 | NDN 4384737 |

UCN 12005Z35 | NDN 4385102 |

UCN 12006M35 | NDN 4385467 |

UCN 12007Z35 | NDN 4385832 |

UCN 12008M36 | NDN 4386198 |

UCN 12009Z35 | NDN 4386563 |

UCN 12010M35 | NDN 4386928 |

UCN 12011Z35 | NDN 4387293 |

UCN 12012M36 | NDN 4387659 |

UCN 12013Z35 | NDN 4388024 |

aatideas.org document updated:

scale | value | ||
---|---|---|---|

UCN | 12019 S19 Yellow | ||

zone(UT) | t339 tt050 | ||

'ICAS in use' can accommodate calendar and clock formatting 'for all people, for all time'. | |||

AD common year day | 139 | ||

G | 2019 May 19 Sunday | ||

UT | 08:08:14 | ||

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