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Any OR gate can be constructed with two or more inputs. It outputs a 1 if any of these inputs are 1, or outputs a 0 only if all inputs are 0. The inputs and outputs are binary digits ("bits") which have two possible logical states. In addition to 1 and 0, these states may be called true and false, high and low, active and inactive, or other ...
A NAND gate is equivalent to an OR gate with negated inputs, and a NOR gate is equivalent to an AND gate with negated inputs. This leads to an alternative set of symbols for basic gates that use the opposite core symbol (AND or OR) but with the inputs and outputs negated. Use of these alternative symbols can make logic circuit diagrams much ...
3-3-2-2-input AND-OR-Invert gate 14 SN74LS54: 74x55 1 4-4-input AND-OR-Invert gate, 74H55 is expandable 14 SN74LS55: 74x56 1 50:1 frequency divider: 8 SN74LS56: 74x57 1 60:1 frequency divider 8 SN74LS57: 74x58 2 3-3-input AND-OR gate and 2-2-input AND-OR gate 14 74HC58: 74x59 2 dual 3-2-input AND-OR-Invert gate 14 US7459A: 74x60 2
E.g. row AB corresponds to the 2-circle, and row ABC to the 3-circle Venn diagram shown above. (As in the Venn diagrams, white is false, and red is true.) The truth table of shows that it outputs true whenever the inputs differ:
For example, a 32-bit integer can encode the truth table for a LUT with up to 5 inputs. When using an integer representation of a truth table, the output value of the LUT can be obtained by calculating a bit index k based on the input values of the LUT, in which case the LUT's output value is the kth bit of the integer.
The AND gate is a basic digital logic gate that implements the logical conjunction (∧) from mathematical logic – AND gates behave according to their truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If all of the inputs to the AND gate are not HIGH, a LOW (0) is outputted.
The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.
The ∧ nodes are AND gates, the ∨ nodes are OR gates, and the ¬ nodes are NOT gates. In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length.