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.

8×1 s=8 s8\times1\ \text{s}=8\ \text{s}
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=4 srate=2 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=8 countdeadTimeTotal=8 sliveTime=4 sobservedRate=2/3 Hz

Dead time is part of the clock budget

The 8 seconds of dead time sit inside a 12 second clock interval.

8 s<12 s8\ \text{s}<12\ \text{s}
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=4 srate=2 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=8 countdeadTimeTotal=8 sliveTime=4 sobservedRate=2/3 Hz