In addition to the explanation others have mentioned, here it is in graph form. See the where the graph of 2^x intersects the y axis (when x=0):
https://people.richland.edu/james/lecture/m116/logs/exponential.html
This also has some additional verbal explanations:
http://scienceline.ucsb.edu/getkey.php?key=2626
The simplest way I think of it is by the properties of exponentials:
2^3 / 2^2 = (2 * 2 * 2) / (2 * 2) = 2 = 2^(3-2)
Dividing two exponentials with the same base (in this case 2) is the same as that same base (2) to the power of the difference between the exponent in the numerator minus the exponent in the denominator (3 and 2 in this case).
Now lets make both exponents the same:
2^3 / 2^3 = 8/8 = 1
2^3 / 2^3 = 2^(3-3) = 2^0 = 1
True on the digit by digit code decryption. That I can forgive in the name of building tension and “counting down” in a visible way for the movie viewer. “When will it have the launch code?!” “In either 7 nano seconds or 12 years…”
If they had been more accurate, it would have looked like the Bender xmas execution scene from Futurama:
https://www.youtube.com/v/aRdRZ6TKo4s?t=25s
I did like the fact that they showed war-dialing and doing research to find a way into the system. It’s also interesting that they showed some secure practices, like the fact there was no banner identifying the system or OS, giving less info to a would be hacker. Granted, now a days it would have the official DoD banner identifying it as a DoD system.
I remember with Windows 95, LAN Manager passwords were hashed in two 7 digit sections which made extracting user password from the password hash file trivial:
https://techgenix.com/how-cracked-windows-password-part1/
Looks like it was worse than I remember. The passwords were first converted to all upper case first!