I am a exempt employee with a salary based on a 40 hour work week. Our company put in our contract that we will put in 96 hours of uncompensated overtime each year. The company gets compensated for this time but the workers do not. If we do not put in this "Green Time" then we are disciplined or terminated. Is this form of overtime considered legal? Can this be considered indentured servitude? Shouldn't my salary be based upon a different time period (whatever 376/52) is? Thank you for your help.

You answered your own question...

If you are exempt and paid on a salary basis then you are paid a fixed amount no matter the quality of work or time it takes to complete it.

So if it takes 50 hours in a week, or 25 hours in a week to do the job, your pay does not change.

Does not matter if your employer bills the client for more than 40 hours, it does not affect your pay.

Conversely, employers can unintentionally do things with the time keeping of exempt employees that may negate exempt status.

I am required to work at least 40 hours a week no matter what. It is on a government contract. I cannot work just 25 hours and expect full pay. We are on the clock as far as the government is concerned but according to the company we are exempt employees. I just think it is a little more complicated than exempt and non-exempt when there are two different realms involved.

What can negate an exempt status in time-keeping?

Here is the FLSA regulation defining "salary basis":
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_541/29CFR541.118.htm

Are you saying your salary is docked if you do not work 40 hours? Or are they just substituting leave time?

Even if (especially if) you are on a govt contract (I assume civilian contractor) your ompany must comply with flsa. Therefore, it is a matter of exempt vs. non-exempt.

Companies can negate exempt staus by not paying the fixed salary amount. In effect, paying hourly, but not paying overtime stating exempt status.

They can also negate exempt status by having employees "clocking" the hours worked.

As stated, you must be paid the fixed salary.

They (the company) will substitute whatever they can (sick time, vacation, floating holiday) until it is used up. Then it goes onto an LWOP (leave without pay) status. Once you have dipped into LWOP it is expected that time is made up or it may result in termination. This is regardless if your tasks and deadlines have been met.

Thanks for that link!!! I will be sure to study that thoroughly as it appears to have a lot of useful info.

Again, read the link I gave you. Once you are out of PTO time, such docking IS legal for full days of absence only, not partial days (unless on intermittent FMLA). And for sick time, if the employer has a plan to replace pay with sick pay benefits, and the amount of days granted is "reasonable" (which has been generally interpreted to be at least 5 days), then they may also dock your salary for full days of sick absence if you have used used your accrual.

I may be confused here on the whole exempt and non-exempt thing. Can somebody please help me out with that?

Yep.
http://www.dol.gov/esa/regs/compliance/whd/fairpay/fs17a_overview.htm

OK I have done a little reading and I have a question about the 1 full workday wording. Is this term meant in succession or is it meant in the compilation of time missed?

In the context of docking your salary? It means you don't come to work at all that day. It is not cumulative, say 2 hours here and 6 hours there.