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How can a 4-bit two's complement operation be implemented using boolean NOR gate? I search lots of 4-bit two's complement videos and articals, but most of them are using XOR gate.

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    $\begingroup$ Two's complement is just a standard how to interpret a number of bits as a number. There is no two's complement operation. 1111 is -1 because I look at it and that's what the label "two's complement" tells me what it is. So what operation are you trying to perform? $\endgroup$
    – gnasher729
    Dec 12, 2022 at 17:57
  • $\begingroup$ NOR is an universal gate, so it can implement any boolean operation. $\endgroup$
    – Rinkesh P
    Dec 13, 2022 at 4:05

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A NOR can serve as an inverter, so 1's complement is easy. Now you need to implement two-bit adders to increment the result. A sum is a XOR ($a\oplus b=\overline{\overline{(\overline{(a+b)}+\overline{(\overline a+\overline b)})}}$, and the carry out an AND ($a\cdot b=\overline{\overline a+\overline b}$).

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Boolean NOR is universal, so you can construct an XOR gate or any other gate from NOR gates, and then use the methods you've read about.

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