Using HC/HCT, AHC/AHCT series logic
The families differ by speed AHC is faster than HC. HCT and AHCT are TTL compatible and HC and AHC are CMOS:


Source: http://www.ti.com/lit/sg/sdyu001ab/sdyu001ab.pdf


Source: http://www.ti.com/lit/sg/sdyu001ab/sdyu001ab.pdf

Also, a useful compatibility chart, CMOS can go 'into' TTL, but TTL cannot go into CMOS (it can't switch it on)


Source: http://www.ti.com/lit/sg/sdyu001ab/sdyu001ab.pdf