Timing Boundary Depth Scans

Dead-Time Count Boundary Three-Row Scan

Detected count changes dead time, live time, and observed rate together. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Four counts leave most of the clock live

Detected count 4 with one second per count uses dead time 4 seconds and leaves live time 8 seconds.

L=12−4×1=8,Ro=1/3L=12\mathbin{-}4\times1=8,\quad R_o=1/3
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=8 srate=1/2 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=4 countdeadTimeTotal=4 sliveTime=8 sobservedRate=1/3 Hz

Six counts split the clock evenly

Detected count 6 with one second per count uses dead time 6 seconds and leaves live time 6 seconds.

L=12−6×1=6,Ro=1/2L=12\mathbin{-}6\times1=6,\quad R_o=1/2
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=6 srate=1 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=6 countdeadTimeTotal=6 sliveTime=6 sobservedRate=1/2 Hz

Eight counts leave four seconds live

Detected count 8 with one second per count uses dead time 8 seconds and leaves live time 4 seconds.

L=12−8×1=4,Ro=2/3L=12\mathbin{-}8\times1=4,\quad R_o=2/3
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