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In sum-of-products (SOP) form, AND gates form the smallest unit and are stitched together using ORs, whereas in product-of-sums (POS) form it is opposite. POS form requires parentheses to group the OR terms together under AND gates, because OR has lower precedence than AND. Both SOP and POS forms translate nicely into circuit logic.
An electronic multiplexer can be considered as a multiple-input, single-output switch, and a demultiplexer as a single-input, multiple-output switch. [3] The schematic symbol for a multiplexer is an isosceles trapezoid with the longer parallel side containing the input pins and the short parallel side containing the output pin. [ 4 ]
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 ...
In optical communication, a reconfigurable optical add-drop multiplexer (ROADM) is a form of optical add-drop multiplexer that adds the ability to remotely switch traffic from a wavelength-division multiplexing (WDM) system at the wavelength layer. This is achieved through the use of a wavelength selective switching module.
Applications of priority encoders include their use in interrupt controllers (to allow some interrupt requests to have higher priority than others), decimal or binary encoding, and analog-to-digital / digital to-analog conversion. [2] Gate-level diagram of a single bit 4-to-2 priority encoder. I(3) has the highest priority.
AND-OR-invert (AOI) logic and AOI gates are two-level compound (or complex) logic functions constructed from the combination of one or more AND gates followed by a NOR gate (equivalent to an OR gate through an Inverter gate, which is the "OI" part of "AOI").
Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: = + ′ ′, where is any Boolean function, is a variable, ′ is the complement of , and and ′ are with the argument set equal to and to respectively.
The carry-select adder generally consists of ripple-carry adders and a multiplexer.Adding two n-bit numbers with a carry-select adder is done with two adders (therefore two ripple-carry adders), in order to perform the calculation twice, one time with the assumption of the carry-in being zero and the other assuming it will be one.