RPU is selected by two criteria: power consumption and timing.
Power consumption in this circuit is desired to be less than 1 mA at 5-V VCC. Since the SN74LVC1G123 has a maximum ICC of 812.5 µA at 5-V VCC, the pull-up resistor must draw less than 187.5 uA. This means that the minimum resistance must be 26.7 kΩ.
For the second criteria, it is reasonable to assume a 15-pF input capacitance and a 5-pF trace capacitance, resulting in a total capacitance of 20 pF. The recovery period for an RC circuit is 5 × R × C. For the case of a 26.7-kΩ resistor, 2 µs is the expected recovery time. Increasing this to 100 kΩ still maintains a very fast recovery time of approximately 8 µs and allows the usage of a standard 5% tolerance resistor. Maintaining a recovery period of less than 1 ms is more than reasonable for this system.
R and C are selected by using the datasheet's graphics and the pulse length equation, tw = K × R × C.
The capacitor value is selected first because there are fewer capacitor values available on the market and this simplifies other calculations. By looking at the figures on the datasheet (some of which are in Section 4.1.1), it can be seen that 0.1 µF was a tested capacitor value that will meet our timing requirement.
The resistor value is calculated from the pulse length equation, tw = K × R × C. By rearranging terms, R = tw / (K × C). K is found in Figure 4-2 to be 0.925 for C = 0.1 µF and VCC = 5 V. Since the pulse width is a range from 1 ms to 25 ms, a range of R values will be given to match. 10.8 kΩ < R < 270 kΩ. 100 kΩ is selected because it is already on our bill of materials from the pull-up resistor and will result in an output pulse of 9.25 ms.