Numeric Std
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Numeric Std
numeric_std is a library package defined for VHDL. It provides arithmetic functions In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function ''f''(''n'') whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their de ... for vectors. Overrides of std_logic_vector are defined for signed and unsigned arithmetic. It defines numeric types and arithmetic functions for use with synthesis tools. Two numeric types are defined: UNSIGNED (represents UNSIGNED number in vector form) and SIGNED (represents a SIGNED number in vector form). The base element type is type STD_LOGIC. The leftmost bit is treated as the most significant bit. Signed vectors are represented in two's complement form. This package contains overloaded arithmetic operators on the SIGNED and UNSIGNED types. The package also contains useful type conversions functions. It is typically included at the top of ...
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VHDL
The VHSIC Hardware Description Language (VHDL) is a hardware description language (HDL) that can model the behavior and structure of digital systems at multiple levels of abstraction, ranging from the system level down to that of logic gates, for design entry, documentation, and verification purposes. Since 1987, VHDL has been standardized by the Institute of Electrical and Electronics Engineers (IEEE) as IEEE Std 1076; the latest version of which is IEEE Std 1076-2019. To model analog and mixed-signal systems, an IEEE-standardized HDL based on VHDL called VHDL-AMS (officially IEEE 1076.1) has been developed. VHDL is named after the United States Department of Defense program that created it, the Very High-Speed Integrated Circuits Program (VHSIC). In the early 1980s, the VHSIC Program sought a new HDL for use in the design of the integrated circuits it aimed to develop. The product of this effort was VHDL Version 7.2, released in 1985. The effo ...
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Arithmetic Functions
In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function ''f''(''n'') whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of ''n''". An example of an arithmetic function is the divisor function whose value at a positive integer ''n'' is equal to the number of divisors of ''n''. There is a larger class of number-theoretic functions that do not fit the above definition, for example, the prime-counting functions. This article provides links to functions of both classes. Arithmetic functions are often extremely irregular (see table), but some of them have series expansions in terms of Ramanujan's sum. Multiplicative and additive functions An arithmetic function ''a'' is * completely additive if ''a''(''mn'') = ''a''(''m'') + ''a''(''n'') for all natural numbers ''m'' ...
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Signedness
In computing, signedness is a property of data types representing numbers in computer programs. A numeric variable is ''signed'' if it can represent both positive and negative numbers, and ''unsigned'' if it can only represent non-negative numbers (zero or positive numbers). As ''signed'' numbers can represent negative numbers, they lose a range of positive numbers that can only be represented with ''unsigned'' numbers of the same size (in bits) because roughly half the possible values are non-positive values, whereas the respective unsigned type can dedicate all the possible values to the positive number range. For example, a two's complement signed 16-bit integer can hold the values −32768 to 32767 inclusively, while an unsigned 16 bit integer can hold the values 0 to 65535. For this sign representation method, the leftmost bit (most significant bit) denotes whether the value is negative (0 for positive or zero, 1 for negative). In programming languages For most architect ...
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Logical Connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective \lor can be used to join the two atomic formulas P and Q, rendering the complex formula P \lor Q . Common connectives include negation, disjunction, conjunction, and implication. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classical compositional semantics wi ...
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Hardware Description Languages
In computer engineering, a hardware description language (HDL) is a specialized computer language used to describe the structure and behavior of electronic circuits, and most commonly, digital logic circuits. A hardware description language enables a precise, formal description of an electronic circuit that allows for the automated analysis and simulation of an electronic circuit. It also allows for the synthesis of an HDL description into a netlist (a specification of physical electronic components and how they are connected together), which can then be placed and routed to produce the set of masks used to create an integrated circuit. A hardware description language looks much like a programming language such as C or ALGOL; it is a textual description consisting of expressions, statements and control structures. One important difference between most programming languages and HDLs is that HDLs explicitly include the notion of time. HDLs form an integral part of electr ...
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