Problems with the key combination "$~1" in my DefaultKeyBinding.dict I have the next DefaultKeyBinding.dict in ~/Library/KeyBindings:

/*
    Key Modifiers
    ^ : Ctrl
    $ : Shift
    ~ : Option (Alt)
    @ : Command (Apple)
    # : Numeric Keypad
*/
{
    "$~1" = ("insertText:", "‖");
}


But when I press the key combination "$~1" (shift+alt+1) I get a little one "ı" and not a double bar "‖". Any solution?
It seems as you are using 'SHIFT'  the one is changed to "!"

try

/*
    Key Modifiers
    ^ : Ctrl
    $ : Shift
    ~ : Option (Alt)
    @ : Command (Apple)
    # : Numeric Keypad
*/
{
 "$~!" = ("insertText:", "||"); 
}