posted January 18, 2007 02:56 PM            

One is NOT the other is OR.

examples:
(A) means NOT(A)
A B means A OR B
(A B) means NOT(A OR B)

You can use any number of A B and nesting pairs of brackets

How would you express A AND B ?
How would you express A XOR B ?

posted January 18, 2007 03:17 PM            

------------------
thinBasic forum
eros.olmi@thinbasic.com

posted January 18, 2007 04:10 PM            

((A) (B))
(((A) (B)) (A B))

posted January 18, 2007 04:57 PM            

2.) It seems to me that there is only one operator in yours
minimalistic language called - it is brackets them self
( ). They negate everything what is inside the brackets.

Very interesting, regards,
Maciej

Edited:
I think Donald spoted it very well (he posted his observation
while I have been typing - regards Donald!) - it is NOR gate
logic. Lack of brackets produces OR logic.
------------------

posted January 18, 2007 05:14 PM            

There is no typing error - the third line follows from the first two and wasn't required.

Added: No need. Just checked Simon's post. Well done, Simon.

posted January 19, 2007 02:14 AM            

quote:

---

How would you express A AND B ?
How would you express A XOR B ?

---

Replace "AND" and "XOR" with OR-NOT combination:

#COMPILE EXE
#DIM ALL
'
TYPE bf
    a AS BIT*1 IN BYTE
    b AS BIT*1
    r AS BIT*1
    ra AS BIT*1
END TYPE
'
FUNCTION PBMAIN () AS LONG
    LOCAL var AS bf
    LOCAL sRes AS STRING
    '
    var.a=1  ' play here all possible combination
    var.b=0  ' play here all possible combination
    sRes="a="+STR$(var.a)+$CRLF
    sRes=sRes+"b="+STR$(var.b)+$CRLF+REPEAT$(40,"-")
    '
    '---- realization AND with help only OR-NOT---------------------------------------
    var.r=NOT(NOT(var.a) OR NOT(var.b)) 'same as (a AND b)
    var.ra= var.a AND var.b  ' test with real AND
    sRes=sRes+$CRLF+"AND based on OR-NOT combination ="+STR$(var.r)+$CRLF+"real (a AND b) = "+STR$(var.ra)+$CRLF+REPEAT$(40,"-")
    '
    '-----realization XOR with help only OR-NOT----------------------------------------
    var.r = (NOT(NOT(NOT(var.a)) OR NOT(var.b))) OR (NOT(NOT(var.a) OR NOT(NOT(var.b))))
    var.ra= var.a XOR var.b  ' test with real XOR
    sRes=sRes+$CRLF+"XOR based on OR-NOT combination ="+STR$(var.r)+$CRLF+"real (a XOR b) = "+STR$(var.ra)
    '-----------------------------------------------------------------------------------
    ? sRes,,"Test"
END FUNCTION
                     

------------------
-=Alex=-

posted January 19, 2007 04:40 AM            

AND ( (A) (B) )
XOR ( ( (A) (B) ) (A B) )

and Alex has demostrated the PB equivalent.

If you are interested in this kind of minimalism then:

http://www.lawsofform.org

posted January 19, 2007 04:55 AM            

it can be done as

  var.r = NOT(NOT(NOT(var.a)) OR NOT(var.b))) OR (NOT(NOT(var.a) OR NOT(NOT(var.b))) 'main 1
  var.r = NOT(NOT(var.a) OR var.b) OR NOT(var.a OR NOT(var.b))       ' main 2
  var.r = not(not(not(var.a) or not(var.b) ) or not(var.a or var.b)) ' variant by Simon Morgan

result is the same.

More intersting result can be done with help of card of Carno

#COMPILE EXE
#DIM ALL
'
TYPE bf
    x1 AS BIT*1 IN BYTE
    x2 AS BIT*1
    x3 AS BIT*1
    x4 AS BIT*1
    y1  AS BIT*1
    y2  AS BIT*1
END TYPE
'
FUNCTION PBMAIN () AS LONG
   LOCAL var AS bf
   '
   var.x1=0
   var.x2=0
   var.x3=0
   var.x4=1
 'assume we have logical expression as
 var.y1=(var.x1 AND var.x2 AND var.x3 AND var.x4) OR _
        (NOT(var.x1) AND var.x2 AND var.x3 AND var.x4) OR _
        (var.x1 AND NOT(var.x2) AND var.x3 AND var.x4) OR _
        (var.x1 AND NOT(var.x2) AND var.x3 AND NOT(var.x4)) OR _
        (NOT(var.x1) AND NOT(var.x2) AND var.x3 AND var.x4)
        '
 'by plaing on cards of Carno(Karno) we can simplify  expression to
 '
 var.y2=(var.x3 AND var.x4) OR (var.x1 AND var.x2 AND var.x3)
 '
 ? "var.y2="+STR$(var.y2),,"var.y1="+STR$(var.y1)
END FUNCTION

Sometimes its very helpful for optimization by speed.

------------------
-=Alex=-