When you ake an exchange on a centralized exchange they will just update your balances on their database. They will subtract 1 btc from your btc balance and add the equivalent in your eth balance. The transaction will not be made on-chain.
When you make a deposit, the coins you send to the receiving address will likely be moved to another address (cold wallet). So, tracking the address on a block explorer is pointless as it will not reflect the operations you made on the exchange.