Logic gates
The seven gates NOT, AND, OR, NAND, NOR, XOR and XNOR: truth tables, equations, reading a small circuit, NAND universality and bitwise operators with their masks.
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- 5 topics
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Each topic is weighted the way the exam weighs it.
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A few cards from the deck
Logic gate: what is it?
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An electronic component that computes a Boolean function: it takes one or more levels, 0 or 1, and returns one.
A gate takes a few transistors, and a modern processor holds billions of them: every computation boils down to gates.
The two inputs of a NAND gate are tied together. Which gate does this behave like?
- NOT
- AND
- OR
- XOR
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NOT
With A = B, NAND(A, A) = NOT(A AND A) = NOT A. This is the first step in building every gate from NANDs.
An AND gate outputs 1 only if … its inputs are 1; an OR gate outputs 0 only if … its inputs are 0.
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An AND gate outputs 1 only if all its inputs are 1; an OR gate outputs 0 only if all its inputs are 0.
The two gates mirror each other: AND demands everything, OR is satisfied by a single 1.
Truth table: what is it?
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A table that gives the output of a logic function for every possible combination of its inputs.
With n inputs it has 2 to the power n rows: 4 for a two-input gate, 8 for a three-input circuit.