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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. Generally, the circuit is constrained to a minimum chip area meeting a predefined response delay.
In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include: Simplification of algebraic expressions, in computer algebra; Simplification of boolean expressions i.e. logic optimization
Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. Informally, a quantified statement " ∃ x {\displaystyle \exists x} such that … {\displaystyle \ldots } " can be viewed as a question "When is there an x {\displaystyle x} such that … {\displaystyle \ldots ...
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule : when p =T (the hypothesis selects the first two lines of the table), we see (at column-14) that p ∨ q =T.
Given the truth table of a logical function, it is possible to write the function as a "sum of products" or "sum of minterms". This is a special form of disjunctive normal form . For example, if given the truth table for the arithmetic sum bit u of one bit position's logic of an adder circuit, as a function of x and y from the addends and the ...
In NMOS logic, the lower half of the CMOS circuit is used in combination with a load device or pull-up transistor (typically a depletion load or a dynamic load). AOI gates are similarly efficient in transistor–transistor logic (TTL). Examples. CMOS 4000-series logic family: CD4085B = dual 2-2 AOI gate [4] CD4086B = single expandable 2-2-2-2 ...