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SN74AHCT02: Input TrTf

Part Number: SN74AHCT02
Other Parts Discussed in Thread: SN74HCS02, SN74LVC1G98, SN74AHCT541

Dear Team,

Our customer is considering to use SN74AHCT02.

They confirmed input Tr/Tf of SN74AHCT02.
As this result, 
 Tr was 56.3ns between 0.8V to 2.0V.
 Tf was 75.3ns between 2.0V to 0.8V.

They thought it's a little slow.
They are concerned about false positives due to the effects of noise.
How should I get rid of this concern?
Should we be provide summit Triger device?

Best Regards,
Seijiro Matsuoka