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Could anybody please explain how the nanosec is being updated. My understanding is that the value has to increase in each cycle.

The current time is the seconds + nanoseconds. Notice that when nanosec decreased it's because sec increased by 1.

To calculate the difference between two times you'll need to get the difference between the sum of those two. Thankfully there's already rclcpp::Time and rclcpp::Duration classes to handle that. Create two instances of rclcpp::Time for the start time and end time, then subtract the two to get an rclcpp::Duration containing the difference.