Each detected pulse can make the detector unavailable for a short recovery interval, so accepted counts reserve part of the observation clock. The dead-time total is exact only for the declared count, fixed recovery time, and non-overlapping bookkeeping; real detectors add pulse pileup, variable recovery, threshold settings, afterpulsing, and timing measurement uncertainty.
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.