TTL (including LSTTL) inputs default to a logic high when not connected. However, it's bad practice to leave them that way as they are susceptible to noise. LSTTL inputs can be tied directly to Vcc or GND. Typical practice held over from the 74xx and 74Sxx days is to use a 10k pull-up or 100 ohm pull-down, a strategy that persists as it helps testability.
More here: 10k Resistor Pull Up/Down Standard for 74 series chips
Now you mentioned you're considering converting the circuit to CMOS. There's two issues with that:
- Unused inputs need to be tied off. It's ok to tie CMOS inputs directly to Vcc or GND, no resistors needed, unless you want them for testability.
- CMOS (AC, HC) input-high levels aren't compatible with TTL: CMOS needs 2/3 Vcc (3.33V) as Vih, which is higher than what LSTTL guarantees (2.7V).
Related: In general, is 5V CMOS compatible with 5V TTL?
The first trouble spot in your diagram as shown is where U6D (74LS00) is driving U1A (74LS74). That's not going to work with an 'HC74 or 'AC74 part: the 'LS00 output-high level isn't enough. You can fix this one of two ways:
Use 74HCT74 or ACT74 device which have TTL-compatible input levels, or
Add a pull-up (about 2k or so) to the 'LS00 to bring bring its output-high up to 'HC or 'AC CMOS level.
Then, tie the unused CMOS inputs to Vcc or GND as needed.
Another trouble spot: if you replace the 74LS193 with an HC type, make sure the UP pin gets a high enough level (2/3 Vcc or better), or use an HCT device. And again, tie off the unused inputs as you need them.
And finally, a really janky trouble spot: the U7 reset chip is open-collector, yet there is no pull-up on its output. Instead, it is relying on the ‘LS74 "R" input for its pull-up, and it’s tied together with the ‘LS163 "CO" through a resistor as a rather stupid kind of wire-or. That’s terrible design, even with LS, and won't work with a CMOS 74HC or HCT74. Instead, replace ROFF4 with a Schottky diode (BAT54 or similar) and add a pull-up to the U7 reset chip output.