A detected pulse occupies a short recovery interval. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Each accepted count reserves a dead-time interval
The detector records 8 counts, and each count reserves 1 second of dead time.
8×1s=8s
Dead time is part of the clock budget
The 8 seconds of dead time sit inside a 12 second clock interval.