The motional mode is a finite packet ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Motion is counted by packets on a finite ladder

The mode spacing is 2 joules per packet.

Epacket=2 JE_{\text{packet}}=2\ \text{J}
Motional packet spacingThe spacing label is checked against the motion ledger.lowerEnergy=0 JupperEnergy=8 JqubitGap=8 JpacketIndex=2 packetmodeSpacing=2 JmotionalEnergy=4 JreadoutBit=1 bit

Packet index two carries four joules of motion

At packet index 2, the motional energy is 4 joules.

22=4 J2\cdot 2=4\ \text{J}
Motional packet indexThe packet index and motional energy are checked together.lowerEnergy=0 JupperEnergy=8 JqubitGap=8 JpacketIndex=2 packetmodeSpacing=2 JmotionalEnergy=4 JreadoutBit=1 bit