![]() The registered var package_install.results contains a list of dictionaries (or maps/hashes - please correct me if I am wrong) with the data related to each package installation. Msg: 'Package installed: jorgelbg/tap/pinentry-touchid' Msg: 'Package already installed: pam-reattach' AĪn EX-NOR gate is a logic gate that gives high output if the inputs are same, otherwise it gives low output.I am installing list of packages in ansible registering variable and outputting it with debug: : AĪn XOR gate is a logic gate that gives high output if the inputs are different, otherwise it gives low output. AĪn NOR gate is a logic gate that gives high output if both the inputs are low, otherwise it gives low output. ![]() AĪ NAND gate is a logic gate that gives a low output only if all its inputs are high, otherwise it gives high output. A plus ( ) is used to show the OR operation. AĪn OR gate is a logic gate that gives high output if at least one of the inputs is high. A dot (.) is used to show the AND operation. ![]() AĪn AND gate is a logic gate that gives a high output only if all its inputs are high, otherwise it gives low output. The following are the logic gates − NOT GateĪ NOT gate inverts a single bit input to a single bit of output. $F '(x, y, z) = \pi (3, 5, 6, 7)$ Logic Gatesīoolean functions are implemented by using logic gates. Hence,į(list of variables) = $\pi$ (list of 0-maxterm indices).į'(list of variables) = $\pi$ (list of 1-maxterm indices). Any Boolean function can be expressed as a product of its 0-maxterms and the inverse of the function can be expressed as a product of its 1-maxterms. ![]() $F'(x, y, z) = \sum (3, 1, 2, 4) = \sum (1, 2, 3, 4)$ The Product of Maxterms (POM) or Product of Sums (POS) formĪ maxterm is addition of all variables taken either in their direct or complemented form. Now we will find the complement of $F(x, y, z)$ Let, $F(x, y, z) = x' y' z' x y' z x y z' x y z $ Hence,į (list of variables) = ∑ (list of 1-minterm indices)į' (list of variables) = ∑ (list of 0-minterm indices) A Any Boolean function can be expressed as a sum of its 1-minterms and the inverse of the function can be expressed as a sum of its 0-minterms. The Sum of Minterms (SOM) or Sum of Products (SOP) formĪ minterm is a product of all variables taken either in their direct or complemented form. \sim B$ Canonical Formsįor a Boolean expression there are two kinds of canonical forms − Each Boolean expression represents a Boolean function.Įxample − $AB’C$ is a Boolean expression. A Boolean expression is composed of a combination of the Boolean constants (True or False), Boolean variables and logical connectives. Boolean FunctionsĪ Boolean function is a special kind of mathematical function $f: X^n \rightarrow X$ of degree n, where $X = \lbrace \rbrace$ where $F(0, 0) = 1, F(0, 1) = 0, F(1, 0) = 0$ and $F(1, 1) = 0$ Boolean ExpressionsĪ Boolean expression always produces a Boolean value. The earliest method of manipulating symbolic logic was invented by George Boole and subsequently came to be known as Boolean Algebra.īoolean algebra has now become an indispensable tool in computer science for its wide applicability in switching theory, building basic electronic circuits and design of digital computers. It deals with variables that can have two discrete values, 0 (False) and 1 (True) and operations that have logical significance.
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