crsunu,
You need to wire it differently.
There are 2 common anodes, 1 for each digit.
There are 8 segment pins, shared between digits. These can come out of 1 shift register.
To get started, connect the 2 anode pins to arduino outputs. You will have to rewrite the code to shift out the segment info, turn on 1 anode, wait 5mS, turn it off, change the segment info, turn on the 2nd anodem wait 5mS, turn it off, repeat. Your eyes will see them as both being on.
Since the anodes will be driven by arduino pins, you will have to limit the amount of current supplied, to <=5mA/segment, with a current limiting resistor per segment.
Assuming you have the UltraRed LEDs, the resistor should be (5V-1.9V)/.005 = 620 ohm. Use that or higher to avoid damaging the pins driving the anodes.
void loop() {
for (int i = 0; i < 100 ; i++) {
// move code here to split into 1, 10s
// hang out for a bit to show the number:
int x = 0;
while (x<10000){
// shrink void DisplayNumber to only show 1 digit
turn off anode 2
DisplayNumber(ones);
turn on anode 1
delay(5);
turn off anode 1
Display(tens);
turn on anode 2
delay(5);
x=x+1;} //
} // next number
} // end loop
Using the while (x<10000) is kind of kludgy. Once you get the numbers working, visit Blink Without Display and use millis() to capture the time passing and turn the digits on/off based on elapsed time instead.
Make sense?