The detonation switches on the bombs worked like this:

• The bombs were connected to the planes with wires. These "pull-out" wires disengaged from the bomb when the bombs were dropped. This started the arming sequence.

• The first step in the arming sequence was a timer. These were just clock circuits that waited 45 seconds before turning on the next step.

• The next step in the sequence was a barometric switch. These were pressure-sensitive devices that detected changes in air pressure. They were not precise but could tell when the bomb was below 5,000 feet in altitude. When it was, they then signaled that the next step in the sequence could start.

• The final step were small radar antennas of the Yagi design, known as "Archies." They bounced radio waves at the ground. They had pre-calibrated these so that when the right reading came it, it was at the desired altitude. When they decided that the right altitude had been reached, they sent a signal to the firing mechanisms and began the atomic detonation itself.

Note that there were multiples of each of these systems and the switches for redundancy, and that some of them (the baros and the Archies) had to "vote" to make sure that no one switch was getting weird readings.

As for why they were split up like this, the clock switches were to make sure the bombs cleared the planes before trying to take readings; the baro switches were to make sure that enemy radar-jamming device couldn't disrupt the Archies before the bomb was at least roughly at the right height.