How will a TTL input behave very close to its high/low bounday?
The switching threshold voltage for a TTL input is undefined.  It may vary between parts, and between makers (or vintage) for a given part.

If your analog signal is near the threshold voltage for the input, the part may oscillate randomly, considering the input as a High at one moment, Low at another.

If you really must send an analog signal to a digital (TTL or CMOS) input, you should really use a Schmidt Trigger input.  The Schmidt Trigger has different thresholds for switching High and Low, so shouldn't oscillate for signals near or between the threshold voltages (but the threshold voltages are still undefined).