How can my calculator do this?

Question

I recently bought a calculator --- a basic one with these keys:

$\;$AC$\;\,$ %$\,$ sqrt
MRC M- M+$\;$ CE
$\;\;$7$\;\;\,$ $\;$8$\;$ $\;\,$9$\;\,$ $\;$÷$\;$
$\;\;$4$\;\;\,$ $\;$5$\;$ $\;\,$6$\;\,$ $\;$x$\;$
$\;\;$1$\;\;\,$ $\;$2$\;$ $\;\,$3$\;\,$ $\;$-$\;\,$
$\;\;$0$\;\;\,$ $\;$.$\;\,$ $\;\,$=$\;\,$ $\;$+$\;$

The MRC key serves as both Recall and Memory Clear. If you press it after a different key, it copies the memory's contents M into the display D. If you press it twice in a row, it does that then clears the memory.

AC puts 0 into D and clears any ongoing calculation there might have been, but leaves M intact.

Some examples of operations on this calculator, and their results. (AC is pressed before each, to clear any previous calculation.)

9+8x7= 119 (no BODMAS/PEDMAS here!)

4x9sqrt= 12

9+1= 10 4= 5

9-1= 8 4= 3

9x8= 72 7= 63

3x2== 18

6÷2= 3 14= 7

1+2= 3 += 5 += 8 += 13 += 21

9-1= 8 -= -7 -= 15 -= -22 -= 37

8-3=+= 8

8-3=-= -2 = -7

7+5% 7.35

7-5% 6.65

7*5% 0.35

7÷5% 140

MRCMRC9M+ 9 8x7M+ 56 MR 65

If you do two or more operator-key presses in a row, only the last one has any effect:

9x-7= 2

There are a couple of deficiencies in this calculator. For example, it has no "change sign" key. Any decent calculator will have a key (possibly marked +/- or (-) which changes the sign of D, leaving M unchanged.

And although it has M- and M+, it has no "store" key (possibly marked STO or M on other calculators). This would copy D into M, leaving D unchanged. Some calculators with memory even have an "exchange" function, which swaps the values of D and M.

So, on this calculator, in as few strokes as possible,

• How do you do "change sign"?
• How do you do "store"?
• How do you do "exchange"?

Answer 1

• How do you do "change sign"?

-0-= (4 strokes)

Basically calculates $0-D=-D$

• How do you do "store"?

-MRCM+(MRC) (3 or 4 strokes)

Calculates $D-M$, then stores $M+(D-M)=D$

• How do you do "exchange"?

-0-M-+MRCM- (7 strokes)

Calculates $-D$, stores $M-(-D)=M+D$, then calculates $-D+(M+D)=M$, then stores $(M+D)-M=D$

Answer 2

First answer (to change sign) could be (if I've understood correctly):

x2=-=
(the idea is to double the number and then subtract it from the original number. Obviously, wouldn't work if you're within a factor of 2 of the largest number the calculator can handle)

Second (to put D into memory)

Starting with M in memory (possibly blank) and D on the display
x2=-= (to make it -D on the display (or whatever the best solution to #1 is)
M- (-D on display, M+D in memory)
+MRC= (M on display, M+D in memory)
MRC (D on display, D in memory)

Third (to do an exchange) could be:

Starting with M in memory and D on the display
x2=-= (to make it -D on the display (or whatever the best solution to #1 is)
M- (-D on display, M+D in memory)
+MRC= (M on display, M+D in memory)
M- (M on display, D in memory)

Answer 3

Now these are my initial guesses. I may have gotten the entire idea wrong, and haven't debugged these at all. But anyways:

Changing signs (assuming unknown memory contents):

Four keypresses: x - 1 = (several alternatives exist)

Alternative, since negative number input doesn't exist: x 2 - = (EDIT: this may be mistaken)

assuming pre-zeroed memory this might work:

two keypresses: M- MRC

Store (assuming unknown memory contents):

four keypresses - MRC M+ MRC

assuming pre-zeroed memory:

one keypress: M+

Swap (assuming unknown memory contents):

(there must be an easier way) - MRC = M+ - MRC x - 1 =

Edited down to 8 presses, still seems to have room for improvement: M+ - MRC M- x 2 - = (re-edited for the sign change)

EDIT: Got rid of the "=" by starting with the negation. 7 keypresses now:
x 2 - M- + MRC M-
Since this is a bit complicated, here's a breakdown of what I think will happen. D is the value on the display, M is original memory contents memory. The "Prev" column is the "previously on display" value, which is used in the calculations, I think.

 Key  Prev  Disp  Mem
  x    ?     D     M
  2    D     2     M
  -    2    2D     M
  M-  2D    -D    M+D
  +   2D    -D    M+D
 MRC  -D   M+D    M+D
  M-  M+D    M     D
 

assuming pre-zeroed memory:

M+ AC