# Ordinals

Ordinals is a scheme for assigning names to satoshis. These names can be linked to digital assets to make them transferrable.

There is an important special case where the two protocol coincide: Recall that an output is a "memory update" if its index is smaller than the number of inputs of the transaction. We call a memory update conservative if it stores the same amount of satoshis as the output that it spends. Conservative updates preserve ordinal ranges.

A Bitcoin Computer smart contract that does not use the _satoshis keyword only produces conservative updates. Therefore a smart objects defined by such smart contracts preserve ordinal ranges.

For example consider an NFT contract:

class NFT extends Contract {
  constructor() {
    super({ data: img })
  }

  send(to) {
    this._owners = [to]
  }
}

If you create an NFT it will be stored in an output and that output is identified by the revision of the smart object. Say that output contains ordinals 5-10 (we are assuming some OrdinalsApi that can return the ordinals stores in a specified output).

const nft = await computer.new(NFT)
const oldOrdinals = await OrdinalsApi.getOrdsFromOutput(nft._rev)
expect(oldOrdinals).to.deep.eq([5, 6, 7, 8, 9, 10])

If we send the NFT it will get a new revision assigned. The important thing is that the new revision will have exactly the same ordinal range.

await nft.send(...)
const newOrdinals = await OrdinalsApi.getOrdsFromOutput(nft._rev)
expect(newOrdinals).to.deep.eq([5, 6, 7, 8, 9, 10])

Therefore you can build smart contracts like swaps that cannot be built with ordinals alone. You can store ordinals inside a smart object, pass them around in smart contracts and safely recover them, for example after they have been exchanged.