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It's a "quad, 2 input nor gate".
To understand the significance of a "nor" gate, you need to understand a little about digital logic.
An "or" gate takes 2 or more digital inputs and if either is "on", the output will be on. (asserted high).
A "nor" gate inverts the output of the "or" gate, meaning that when either of the outputs are "on", the output will be "off" (asserted low).
The two input part of the description just indicates that it only accepts two inputs.
So, simply stated:
If either (or both) input(s) of a quad, 2 input nor gate is (are) asserted high, the output will be low. If both inputs are off (low), the output will be high.
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