function Encode64(S: string): string;
const
  Codes64 = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/';
var
  i: Integer; a: Integer;
  x: Integer; b: Integer;
begin
  Result := '';
  a := 0;
  b := 0;
  for i := 1 to Length(s) do
  begin
    x := Ord(s[i]);
    b := b * 256 + x;
    a := a + 8;
    while a >= 6 do
    begin
      a := a - 6;
      x := b div (1 shl a);
      b := b mod (1 shl a);
      Result := Result + Codes64[x + 1];
    end;
  end;
  if (a > 0) then
  begin
    x := b shl (6 - a);
    Result := Result + Codes64[x + 1];
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  s : String;
begin
  s := Encode64('Show Delphi');
  ShowMessage(s);
end;