A chip fab could cast a single kind of gate and still build every circuit: a NAND with its inputs tied together gives NOT, one more NOT turns that into AND, and inverting both inputs before the NAND yields OR, straight out of De Morgan’s laws. XOR goes high when the two inputs differ, which is exactly the sum bit of one-bit addition, while AND holds the carry — so 1 plus 1 makes 10 in binary. Two cross-coupled NAND gates keep whatever bit was last set even after both inputs are released, and that is where computer memory begins.
A chip fab could cast a single kind of gate and still build every circuit: a NAND with its inputs tied together gives NOT, one more NOT turns that into AND, and inverting both inputs before the NAND yields OR, straight out of De Morgan’s laws. XOR goes high when the two inputs differ, which is exactly the sum bit of one-bit addition, while AND holds the carry — so 1 plus 1 makes 10 in binary. Two cross-coupled NAND gates keep whatever bit was last set even after both inputs are released, and that is where computer memory begins.
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