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Logic circuits are physical representation of simple logic operations, AND, OR and NOT (and their combinations, such as non-sequential flip-flops or circuit networks), that form a mathematical structure known as Boolean algebra. They are complete in sense that they can perform any deterministic algorithm.
In modern circuit engineering settings, there is little need to consider other Boolean algebras, thus "switching algebra" and "Boolean algebra" are often used interchangeably. [ 10 ] [ 11 ] [ 12 ] Efficient implementation of Boolean functions is a fundamental problem in the design of combinational logic circuits.
In his thesis, Shannon, a dual degree graduate of the University of Michigan, proved that Boolean algebra [3] could be used to simplify the arrangement of the relays that were the building blocks of the electromechanical automatic telephone exchanges of the day. He went on to prove that it should also be possible to use arrangements of relays ...
A logic circuit diagram for a 4-bit carry lookahead binary adder design using only the AND, OR, and XOR logic gates.. A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output.
Boolean algebra (structure), a set with operations resembling logical ones; Boolean circuit, a mathematical model for digital logical circuits. Boolean data type is a data type, having two values (usually denoted true and false) Boolean expression, an expression in a programming language that produces a Boolean value when evaluated
In Boolean algebra, a parity function is a Boolean function whose value is one if and only if the input vector has an odd number of ones. The parity function of two inputs is also known as the XOR function. The parity function is notable for its role in theoretical investigation of circuit complexity of Boolean functions.
Usually, the smaller circuit with the same function is cheaper, [2] takes less space, consumes less power, has shorter latency, and minimizes risks of unexpected cross-talk, hazard of delayed signal processing, and other issues present at the nano-scale level of metallic structures on an integrated circuit. In terms of Boolean algebra, the ...
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...