Following the rules of the yellow paper, it costs 4 gas for every zero bytes of transaction data (msg.data). Compare that to the cost of 68 gas, or 17 times as expensive for a non-zero byte. The hamming weight of msg.sender makes no difference tho. The only bytes we are interested in are in msg.data, which includes the function selector.

For example, if you're using the transfer(_to, _amount) method on an ERC20 token, if the receiver address _to contains a lot of zeroes, it will save you gas executing the transaction.

Using OpenZeppelin’s StandardToken as a reference implementation, a standard transfer to an address with zero bytes costs 51,486 gas. However, a transfer to an address with eight zero bytes only costs 50,974 gas, a difference of 51486 — 50974 = 512 gas. This can also be expressed as 64 * 8.

I suggest you read this article On Efficient Ethereum Addresses for a detailed explanation.

Following the rules of the yellow paper, it costs 4 gas for every zero bytes of transaction data (msg.data). Compare that to the cost of 68 gas, or 17 times as expensive for a non-zero byte. The hamming weight of msg.sender makes no difference tho. The only bytes we are interested in are in msg.data, which includes the function selector.

For example, if you're using the transfer(_to, _amount) method on an ERC20 token, if the receiver address _to contains a lot of zeroes, it will save you gas executing the transaction.

Using OpenZeppelin’s StandardToken as a reference implementation, a standard transfer to an address with non-zero bytes costs 51,486 gas. However, a transfer to an address with eight zero bytes only costs 50,974 gas, a difference of 51486 — 50974 = 512 gas, which can be expressed as 64 * 8 (the number of zero bytes).

I suggest you read this article On Efficient Ethereum Addresses for a detailed explanation.