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When a new hosts joins a network and broadcasts to find a DHCP server every host on the netowkr knows of the new hosts and its' request. Does every host also know of the final ACK packet, that acknowledges the assigning of an IP address?

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The DHCP RFC, RFC2131 says:

Normally, DHCP servers and BOOTP relay agents attempt to deliver
DHCPOFFER, DHCPACK and DHCPNAK messages directly to the client using
unicast delivery.
[...]
A client that cannot receive unicast IP datagrams until its protocol software has been configured with an IP address SHOULD set the BROADCAST bit in the 'flags' field to 1 in any DHCPDISCOVER or DHCPREQUEST messages that client sends. The BROADCAST bit will provide a hint to the DHCP server and BOOTP relay agent to broadcast any messages to the client on the client's subnet.

So in normal operation, the DHCPACK message will be unicast (I.E. Layer2 unicast), directed to the client MAC Address.
In a modern, switched, environnement, the other hosts will not see the final ACK.

In an old network that still use hubs, all network interface card in the layer 2 network will still see the related frames, but are not supposed to process them, so they will not transmit them to the operating system unless set in promiscuous mode.

2

Every host sees the DHCPACK but they don't really have anything to do with it, as they know they are not the ones requesting.

Also be aware that not all DHCPOFFER are broadcast, it depends on the BROADCAST bit in the 'flags' field, see RFC2131 here:

A client that cannot receive unicast IP datagrams until its protocol software has been configured with an IP address SHOULD set the BROADCAST bit in the 'flags' field to 1 in any DHCPDISCOVER or DHCPREQUEST messages that client sends. The BROADCAST bit will provide a hint to the DHCP server and BOOTP relay agent to broadcast any messages to the client on the client's subnet. A client that can receive unicast IP datagrams before its protocol software has been configured SHOULD clear the BROADCAST bit to 0. The BOOTP clarifications document discusses the ramifications of the use of the BROADCAST bit [21].

A server or relay agent sending or relaying a DHCP message directly to a DHCP client (i.e., not to a relay agent specified in the 'giaddr' field) SHOULD examine the BROADCAST bit in the 'flags' field. If this bit is set to 1, the DHCP message SHOULD be sent as an IP broadcast using an IP broadcast address (preferably 0xffffffff) as the IP destination address and the link-layer broadcast address as the link-layer destination address. If the BROADCAST bit is cleared to 0, the message SHOULD be sent as an IP unicast to the IP address specified in the 'yiaddr' field and the link-layer address specified in the 'chaddr' field. If unicasting is not possible, the message MAY be sent as an IP broadcast using an IP broadcast address (preferably 0xffffffff) as the IP destination address and the link- layer broadcast address as the link-layer destination address.

Edit:JFL answered while I was tipping this

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