GUI of a Karnaugh Map

I intend to implement a three-variables Karnaugh map with the following code. There are two points I failed to figure out. How to remove the outer double-line border? How to change the toggling into “1” and blank instead of black and white? Please help.

labels = {"00", "01", "11", "10"};
frame = Graphics[{
    Line@Table[{{i, 0}, {i, 4}}, {i, 0, 2, 1}],
    Line@Table[{{0, i}, {2, i}}, {i, 0, 4, 1}], 
    Table[Text[
      labels[[3 - i + 1]], {-0.3, i + 0.3}], {i, {0, 1, 3, 2}}], 
    Table[Text[labels[[i + 1]], {i + 0.75, 4.25}], {i, {0, 1, 0, 1}}],
     Line[{{0, 4}, {-0.75, 4.75}}], 
    Text[Style[ "A B" , 12], {-0.5, 4.}], 
    Text[Style["C", 12], {0., 4.5}]}, ImageSize -> {100, 200}];

Manipulate[
  arrX = ConstantArray[0, {2, 4}];
  EventHandler[
  Dynamic[
   mat = Reverse[ Transpose[arrX]] ;
   Show[frame,
    MatrixPlot[
     mat,
     Mesh -> All,
     ImageSize -> {100, 200},
     PlotRangePadding -> 0,
     FrameTicks -> None,
     ColorRules -> {1 -> Black, 0 -> None}]
    ]],
  {
   "MouseClicked" :> (pos = Ceiling[MousePosition["Graphics"]];
     arrX = ReplacePart[arrX, pos -> 1 - arrX[[Sequence @@ pos]]];
     )
   }], 
 AppearanceElements -> None,
 FrameMargins -> 0
 ]

Manipulate[arrX = ConstantArray[0, {2, 4}];
    EventHandler[Dynamic[mat = Reverse[Transpose[arrX]];
    Show[frame, 
        MatrixPlot[mat, Mesh -> All, ImageSize -> {100, 200}, 
                   PlotRangePadding -> 0, FrameTicks -> None, 
                    ColorRules -> {1 -> None, 0 -> None}], 
        Epilog -> {MapIndexed[If[#1 == 1, 
                                Text[Style[#1, Bold, 20, Red], #2 - {.5, .5}], 
                                Text[""]] &, 
                              arrX, {2}]}]], 
    {"MouseClicked" :> (pos = Ceiling[MousePosition["Graphics"]];
                    arrX = ReplacePart[arrX, pos -> 1 - arrX[[Sequence @@ pos]]];)}], 
   Paneled -> False, AppearanceElements -> None, 
   FrameMargins -> 0] // Panel