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There are many ways to accomplish this but probably the most common is the use of a 'shift register'. A shift register is just a device which takes in the serial binary, and pushes each recorded bit into the next slot in it's 'memory'. so say you are sending an 8-bit number serially, say: 10110110. The shift register would have 8 memory slots, looking like this:

00000000

the digits would usually be transferred right to left, so they'd be sent in this order:

0, 1, 1, 0, 1, 1, 0, 1

sequentially, then out shift register would look like this:

10000000

01000000

10100000

11010000

01101000

10110100

11011010

01101101

once the register saw that it had received 8 bits, it would spit out the 8bit received number: 01101101, which is the mirror image of our original number. If we then take out parallel data lines and send the first one to the eighth, the second to the seventh, etc. we will have:

10110110, our original number, now in parallel format.

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