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These formulas are based on the observation that the day of the week progresses in a predictable manner based upon each subpart of that date. Each term within the formula is used to calculate the offset needed to obtain the correct day of the week. For the Gregorian calendar, the various parts of this formula can therefore be understood as follows:
For determination of the day of the week (1 January 2000, Saturday) the day of the month: 1 ~ 31 (1) the month: (6) the year: (0) the century mod 4 for the Gregorian calendar and mod 7 for the Julian calendar (0). adding 1+6+0+0=7. Dividing by 7 leaves a remainder of 0, so the day of the week is Saturday. The formula is w = (d + m + y + c) mod 7.
Thus in a common year the week number on the doomsday itself is one less if it is a Sunday, i.e. in a common year starting on Friday (such as 2010, 2021, & 2027). Computer formula for the anchor day of a year
Every week belongs to a single year, i.e. there are no ambiguous or double-assigned weeks. The date directly tells the weekday. All week-numbering years start with a Monday and end with a Sunday. When used by itself without using the concept of month, all week-numbering years are the same except that some years have a week 53 at the end.
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For example, if the fiscal year end month is August, the company's year end could fall on any date from August 25 to August 31. In particular, the last fiscal week is the one that includes August 25 and the first fiscal week of the following year is the one that includes September 1. In this scenario, fiscal years would end on the following days:
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