[BryanC]

NAD⁺ is reduced to NADH in the reactions below:

Pyruvate oxidation
NAD⁺ + pyruvate + CoA -> NADH + H⁺ + CO₂ + Acetyl-CoA

3rd step of Kreb's cycle
NAD⁺ + Isocitrate -> NADH + H⁺ + CO₂ + α-ketoglutarate

4th step of Kreb's cycle
NAD⁺ + α-ketoglutarate + CoA -> NADH + H⁺ + CO₂ + Succinyl-CoA

Is there a reason why CO2 is produced when there is a reduction of NAD⁺?

The texts I have so far simply state that CO2 is derived from the carbon atom that is lost in the hydrocarbon molecule. However, that doesn't seem to explain the core reason why this happens.

[Arkcon]

If you get a reduction, how is that accomplished?  What causes a reduction?  https://en.wikipedia.org/wiki/Citric_acid_cycle#Steps

[Babcock_Hall]

I think it helps to assign oxidation numbers to carbon atoms and to tally up electrons.

[Babcock_Hall]

ON (C) = (number of bonds to O, N, etc) - (number of bonds to H).