Understanding pull-up resistors and the 7489 memory chip
R1 - R4 are current-limiting resistors for the LEDs - they are required regardless of what is controlling the LEDs.  If the LEDs drop 2 volts, assume there is 3 volts across the resistors (there's be a bit less, because the 7489 can't pull its outputs quite to ground), then for 20 mA, you'd want 150 Ohms.  LEDs aren't very fussy about current, as long as it is less than their Absolute Maximum rating.  Lower current gives less light, but for indicator light use I find tha 10 mA is more than enough, so I'd use 300 Ohms or more.

4.7K is a common value for general pull-up resistors.  For high-speed signals, a lower value may be required to ensure that the signal changes fast enough when the signal should go high.