The Date of Easter Sunday

The Date of Easter Sunday.

Last updated: 13 July 2024: David Green

1. DEUCE Program ZV02 - Easter Day

DEUCE had a demonstration program ZV02. It "reads a year from the I.D. and displays in the scope the date of Easter Sunday in that year".

Cliff Robinson recalled that: "Easter Program: you may be interested in its background. We were due to formally demonstrate DEUCE to the first batch of experts (mainly from NPL) who were due to come to Kidsgrove. About three days before they came, J. K. Brown insisted we invent and make some demo programs to show it off. One of these was the Easter Sunday program written by John Denison." This event most likely occurred in 1955.

So, clearly, the Easter program was not a Pilot Ace program. However, given the dearth of demonstration programs for the Pilot Ace it is convenient to adapt it to run on the emulator.

To reverse-engineer DEUCE program code to Pilot ACE code can be difficult. DEUCE had 18 temporary stores (TS13, TS14, TS15, TS16, DS19, DS20, DS21, QS17 and QS18) while Pilot Ace had only nine (TS15, TS16, TS20, TS26, TS27, DS12 and DS14). Also DEUCE had 12 delay lines compared with 11 for Pilot Ace. So we are trying to get a quart into a pint pot.

If a DEUCE program used automatic division or the quad stores (especially for AIM) it was probably too unlike an earlier Pilot Ace program for the effort to be worthwhile. However, Easter Day was a very early DEUCE program - number 6 - and the advanced features were not used, so it has been possible to adapt it for the Pilot Ace.

2. The Method Used

Calculation

The program makes no allowance for the change from the Julian to the Gregorian calendar in England in 1752 so correct answers will not be produced for years before 1753. Future dates can be set up to the year 9999.

An algorithm to calculate the day of the week for any Julian or Gregorian calendar date was devised by Christian Zeller in the 19th century date and is known as Zeller's congruence. A list of Easter Sunday dates starting at 1700 can be found at The Astronomical Society of South Australia's web site.

3. Operating Instructions

Initial Input the program cards.
The program stops on {1 0-26 s}
Switch the scope to DL9.
On the ID set the thousands digit of the year (the P_1-9 keys correspond to the digits 1-9, for 0 the ID is zero).
Single shot.
Clear the ID.
Repeat steps 4-6 for the other three digits of the year.
The program stops on {5 28-9 } with the date of Easter Day displayed in the scope.
Single shot to clear the display, clear the ID and return to step 4.

On DEUCE the instructions included two steps to align the scope properly, using a switch on the console. The Pilot Ace did not have this facility so the results may appear anywhere on the screen. This is an unfortunate property of Pilot Ace, not a program error. If you are lucky it will look something like this (for year 1975).

March 30

If you are unlucky it will look something like this (for 1988).

April 3 1988

4. Program Notes

Program cards to run the demonstration on the emulator can be downloaded here and a flow chart of the program is shown below.