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Logic gates can be made from quantum mechanical effects, see quantum logic gate. Photonic logic gates use nonlinear optical effects. In principle any method that leads to a gate that is functionally complete (for example, either a NOR or a NAND gate) can be used to make any kind of digital logic circuit. Note that the use of 3-state logic for ...
Example Boolean circuit. 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.
Sequential logic is used to construct finite-state machines, a basic building block in all digital circuitry. Virtually all circuits in practical digital devices are a mixture of combinational and sequential logic. A familiar example of a device with sequential logic is a television set with "channel up" and "channel down" buttons. [1]
Example of a simple circuit with a toggling output. The inverter forms the combinational logic in this circuit, and the register holds the state. Many digital systems are data flow machines. These are usually designed using synchronous register transfer logic and written with hardware description languages such as VHDL or Verilog.
The AND gate is a basic digital logic gate that implements logical conjunction (∧) from mathematical logic – AND gate behaves according to the truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If not all of the inputs to the AND gate are HIGH, a LOW output results.
The result is a circuit that outputs a 1 when the number of 1s at its inputs is odd, and a 0 when the number of incoming 1s is even. This makes it practically useful as a parity generator or a modulo-2 adder. For example, the 74LVC1G386 microchip is advertised as a three-input logic gate, and implements a parity generator. [13]
For example, the part of an arithmetic logic unit, or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such as half adders, full adders, half subtractors, full subtractors, multiplexers, demultiplexers, encoders and decoders are also made by using combinational logic.
The behavior of OR is the same as XOR except in the case of a 1 for both inputs. In situations where this never arises (for example, in a full-adder) the two types of gates are interchangeable. This substitution is convenient when a circuit is being implemented using simple integrated circuit chips which contain only one gate type per chip.