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I mean I get why 568A-568B works:

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But why does this not-crossed wiring work?

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There are two kinds of equipment: DTE (Data Terminal Equipment) and DCE (Data Communications Equipment). The pins for the DTE transmit are the pins for the DCE receive, and vice versa. If you have one of each type, then you use a straight-through cable, and if you have two of the same kind, you use a crossover cable. At least, that is how it used to be. Today, most equipment can detect what is necessary and will modify itself through negotiation with the other end so that you end up with opposite configurations on each end of the cable.

For network cables on UTP, PCs, printers, and routers are examples of DTE equipment, which are hosts. Hubs, bridges, switches, WAPs, modems, etc. are examples of DCE equipment.

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Traditionally, concentrator devices (hubs, switches) have the receiver and transmitter pins swapped (MDI-X) compared to other devices (MDI used with NICs, router). This requires straight 1:1 cables when connecting an MDI port to an MDI-X one.

Only when you connect to like devices to each other - two hubs, both MDI-X, or two NICs, both MDI - you need to do the swap in the cable, so a crossover cable is required.

Why was this done? Ethernet over twisted pair was designed to re-use the existing category 3 cable plants of that time. These and the existing patch cables were 1:1, so the standard incorporated that. This is different from fiber cabling that generally uses a crossover in each element (vertical, horizontal cabling and patch cables).

Today, this is mostly a thing of the past. Nearly all devices built after ca. 2000 use Auto MDI-X where the sender and transmitter pairs are matched automatically.

Gigabit and faster Ethernet use a pair-matching scheme that theoretically allows you to use arbitrary pairings. In practice, this is not always guaranteed to work, so you're best off with a 1:1 cable most of the time.

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Here's a less technical answer if your interested. Let's forget MDI-X for the moment. MDI-X is the automatic decision process of where to put transmit and receive. Also, I'm not discussing POE because there are diffrent types.

Transmit and receive on 10/100mb are traditionally on the orange and green pair. If your switch transmits on orange your computer needs to receive on orange and vice versa. If the both transmit on the same pair they'd never communicate. The data would collide.

Since two like switches might transmit on orange (it might be green I don't remember) their transmit is going into the other ports transmit. One transmit needs to go to the others receive. That's why you need a crossover cable to connect two switches together for example.

Then came MDI-X. This figures out if the transmit and receive need to be reversed on one end and eliminates the need for a crossover cable. (side note, a cross over cable is a 568A on one end and a 568B on the other (orange and green are swapped)).

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