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Rusty, do mind to ALWAYS make a clear distinction between the "object" and "image" sides! Otherwise confusion will just continue to grow...
One ("object" of course...) is in front of the lens. This is the reality side, where DR (can be) great, and both tone (grade) and spatial (detail) resolution approaches infinity at long integration times (very, very low ISO values in capture). This is the basis for the input DR, you measure what input range in front of the camera in which the camera can accurately still resolve detail.
The other, the "image" side, is the 2-D image that the lens projects on to the sensor or film for the medium to capture. Hopefully the lens lets through at least 11-12Ev's of very good detail material in situations with no or little flare in the glass. At about 15Ev, you're getting severely impeded by random scatter in the glass and the glass surfaces - what we call "veiling flare". The "Image" can be represented by any method or scale that you chose, as long as you KNOW how conversion between input>output was done, you can get back to the original object value.
The image side has to be RECORDED. In practice it has to be translated into some value range that gives you enough tone resolution without taking up to much data space. Raw data is almost always linear, that is - if you double the exposure, you double the raw value. 1-2-4-8-16-32-64-128-256-512-1024-2048-4096-8192-16384 - those are the 14 full steps in a 14-bit raw file. Note that EV3 goes from 4 to 8, that is 4 discrete "steps" of tone resolution. Look further up, at EV11 that goes from 2048 to 4096 - that's 2048 steps of tone resolution in one Ev!
Now, if you convert that by using a gamma of "2.0", close to standard, into the discrete levels of 1=1, 2=2, 3=4, 4=8, 5=16, 6=32, 7=64, then you only need 14 bit steps - that 4 bits! - to cover all 14 Ev's of input! But your tone resolution will be atrocious, you'll have serious posterizing. Only 14 gray scale levels.
But! Now those four bits actually "cover" 14Ev of the original object DR you put in to the system... 4bit = 14Ev DR in this case!
jpg uses 8 bits, 256 discrete levels, which is enough to get rid of almost all posterizing - but it doesn't leave much room for added pulling or pushing without making the discrete steps visible.