Live time is the part of the observation clock still available after recorded dead-time intervals have been reserved. The subtraction is exact only for the stated clock, dead-time total, and ideal partition model; real instruments require accounting for overlapping pulses, variable electronics recovery, trigger thresholds, and timing jitter.
Dead time and live time partition the observation clock. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Live time is the clock time left after dead time
The clock has 12 seconds, and dead time uses 8 seconds.