Final answer:
The correct conversion approach is called Parallel Conversion, which involves running both the old and new systems simultaneously until the new one is verified as reliable.
Step-by-step explanation:
The conversion approach in which the old and new systems are operated side by side until the new one proves to be reliable is called Parallel Conversion. This strategy minimizes risk by allowing comparison between the performance of the old system and the new system over a period of time. It also provides a contingency plan, wherein if the new system fails, the old system can still be used without disrupting the organization's operations.