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Multiplexers can also be used as programmable logic devices, to implement Boolean functions. Any Boolean function of n variables and one result can be implemented with a multiplexer with n selector inputs. The variables are connected to the selector inputs, and the function result, 0 or 1, for each possible combination of selector inputs is ...
A CMOS transistor NAND element. V dd denotes positive voltage.. In CMOS logic, if both of the A and B inputs are high, then both the NMOS transistors (bottom half of the diagram) will conduct, neither of the PMOS transistors (top half) will conduct, and a conductive path will be established between the output and Vss (ground), bringing the output low.
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.
Logic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in digital electronics and integrated circuit design.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
The Boolean logic for the sum (in this case ) will be whereas for the carry will be . With the addition of an OR gate to combine their carry outputs, two half adders can be combined to make a full adder. [2] The truth table for the half adder is:
Symbol for 4-4 AOI gate. Real world examples of an 4-4 AOI gate is found in the CD4048B logic IC (see further below). [7]The 4-4 AOI gate can be represented by the following boolean equation and truth table:
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.