Strictly adhering to Lachman's Maxim (Complexity is a diseconomy of scale),
 this method is designed to run super-bly as a stand-alone routine when the
 the most BASIC of computer is the only resource--meaning minimal operating
 system functionality beyond superBASIC as a command-line interpreter, and
 no integer, nor floating point, variables.

 It succeeds where other Methods do not when computing the day of the week
 on lowly 8-bit-bus systems: having no need of C compilers which run on
 bloated development systems as for Michael Keith's and others'.


Given:

D$    as a Date stamp YEARMoDa in basic ISO format
T$    as an Offsets' table;
F$    as a Flag to choose between Julian (=0) & Gregorian (=1)

the superBASIC routine below is to compute:

s$    as the offset year 
g$    as the Gregorian Offset to a Julian result
w$    as the mod 7 day-number compatible with ISO 8601:            
      Sun=0  Mon=1  Tue=2  Wed=3  Thu=4  Fri=5  Sat=6.

REM Step 0 - defines the Offsets' table & the offset year:
LET T$="400351362402" : s$=INT(D$/10000-.03) 

REM Step 1 - calculates Gregorian Offset:
LET g$=(s$DIV 100)&"32"DIV 16 *F$

REM Step 2 - computes the day-number within the week:
LET w$=(s$DIV 4+ D$(1TO 4)+ T$(D$(5TO 6))+ D$(7TO 8)+ g$)MOD 7

This routine is valid for Gregorian dates as of 15.oct.1582, and for
historical Julian dates from 1.mar.1 until 4246 A.D.

--

      REFERENCES

http://terdina.net/ql/ql.html
http://www.guernsey.net/~sgibbs/roman.html 
gopher://gopherite.org/0/users/retroburrowers/TemporalRetrology/cc/os