GB/T 5271.2-1988 Data Processing Vocabulary Part 02 Arithmetic and Logical Operations GB/T5271.2-1988 Standard Download Decompression Password: www.bzxz.net

1.1 Introduction
National Standard of the People's Republic of China
Data processing vocabulary
Part 02: Arithmetic and
logic operations
UDC 681.3:001.4
GB 5271.2-88
This vocabulary consists of about twenty parts. This part explains some commonly used mathematical and logical concepts in data processing. Some concepts about numerical quantities are explained according to the calculation methods used. This part also includes general terms for arithmetic and logical operations. In Appendices A (reference) and B (reference) of this part, there are tables of Boolean operations of one and two variables, and the symbols representing these operations are listed in the tables. These symbols are not standard. In Appendix C (reference), the terms and definitions related to pure mathematics are supplemented. This part of the vocabulary is equivalent to the international standard ISO2382/2--1976 "Data processing - Vocabulary Part 02: Arithmetic and logical operations".
1.2 Scope
This vocabulary selects terms and concise definitions of some concepts in the field of data processing, and clarifies the relationship between different concepts. In order to facilitate domestic and international exchanges.
The vocabulary covers all major aspects of data processing, including the main processing processes and types of equipment used, data representation, data organization, data description, computer programming and operation, peripheral equipment, data communication and other special applications. 1.3 Scope of application
This standard applies to the design, production, use, maintenance, management, scientific research, teaching and publishing of various fields related to electronic computers and information processing.
2 Principles and rules to be followed
The following rules have been explained in detail in Part - (i.e. GB5271.1-8501 Basic Terms). They are also applicable to this part and will not be repeated here. Only the titles of the items are listed as follows: 2.1 Definition of terms,
2.2 Composition of terms;
2.3 Classification of terms;
2.4 Selection of terms and definition of terms; | |tt||2.5 Polysemy;
2.6 Abbreviations;
Use of parentheses;
2.8 Use of square brackets;
2.9 Use of boldface terms and asterisks in definitions; Approved by the Ministry of Electronics Industry of the People's Republic of China on April 20, 1988, and implemented on May 1, 1989
2.10 Spelling;
2.11 Compilation of index tables.
3 Terms and definitions
02 Arithmetic and logical operations
02.01 Methods
02.01.01 Heuristic method GB 5271. 2-88
A method of exploring solutions to problems, which gradually approaches a satisfactory final result by evaluating a series of approximate results, such as a purposeful trial and error method. 02.01.02
mathematical inductionA method of proving a proposition involving a series of terms related to a natural number not less than N, by first verifying that the terms related to N hold, then assuming that the terms related to a natural number n not less than N hold, and then proving that the terms related to n plus 1 also hold.
formal logic
the study of the form and structure of valid arguments, without regard to the meaning of the objects involved in the arguments. symbolic logic, mathematical logic02.01.04
a discipline in which valid arguments and operations are performed in artificial languages ​​to avoid the ambiguity and logical unsuitability of natural languages.
02.02 Variable representation
Logical variable, switching variablelogic variable, switching variable02.02.01
A variable that can take only a finite number of possible values ​​or states. Example: A variable that takes any character in a character set. 02.02.02
Argument, independent variableargumcent
An independent variable.
02.02. 03
Value of an argumentValue of an independent variable
argument
Any value of an independent variable.
Example: A search keyword; a number that identifies the position of an item in a table. Parameterparameter
02- 02. 04
A variable that can be assigned a constant value for each specific application or can be used to identify an application. 02.02.05
scalar
a quantity represented by only one value.
02. 02. 06
02. 02. 08
vector
a quantity represented by an ordered set of scalars. span
the difference between the maximum and minimum values ​​that a quantity or function can take. characteristic(of a logarithm)the integer part of a logarithmic expression, which can be positive or negative. mantissa(of a logarithm)02.02.09
the nonnegative fractional part of a logarithmic expression.
natural number, nonnegative integernaturalnumber, nonnegaiveintegernumber 0.1,2,.…
Note: Some people define natural numbers as starting from 1, not from 0. 23
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02.03.02 integer integer, integer number 0, +1, 1, +2, -2, among
real number real number
02. 03. 03
a number that can be represented by a finite or infinite number of digits in a fixed base number system. 02.03.04 rational number rational number A real number that is the quotient of a non-zero integer divided by another integer. 02.03.05 irrational number irrational number A real number that is not a rational number.
complex number complex number
a number that can be composed of a pair of ordered real numbers and can be represented in the form of α+bi, where α and b are real numbers and i21. Random number random number
02.03.07F
A number selected from a known set of numbers, in which each number has the same probability of appearing. Random number sequence random number sequence02.03.081
A sequence of numbers in which each number cannot be predicted based solely on the numbers preceding it02.03.09 Pseudo-random number sequence pseudo-random number sequence A sequence of numbers that is obtained using a given algorithmic process, but for some requirements, it can be effectively used as a random number sequence.
02.03.10 Serial number serial number
An integer identifying the position of an item in a sequence. 02.03.11 Zero (in data processing) zero (in data processing) A number that, when added to or subtracted from any number, produces the same result as the original number. Note: In computers, zero can be represented in different ways, such as positive zero, negative zero (which can be obtained by subtracting a signed number from itself), and floating-point zero (in floating-point representation, the fixed-point part is zero, and the order can take different values). 2 binary [ternary octal decennial decennial decennial decennial decennial decennial N-ary], binary [ternary octal 02.03.12
decennial] [ ...03.13 Binary [ternary octal decimal dodecimal hexadecimal [N-ary] binary [ternary octal Ldecimal or denary duodecimal Lsexadecimal or hexadecimal JN-ary] refers to a fixed radix number system with a radix of two [three eight twelve sixteen N. 02.03.14 Factorial factorial
The product of the successive multiplications of natural numbers 1, 2, 3, ... up to and including a given integer. 02.04 Functions and mappings
02. 04. 01
Logic function, switching function logic function, switching function A function in which each of its arguments and the function itself can have only a finite number of possible values. 02.Q4.02 Boolean function A logic function in which each of its arguments and the function itself can have only two possible values. 02.04.03 recursively defined sequence A sequence of terms, in which the terms after the first term are determined by operations in which the objects of operation include some or all of the previous terms.
Note: In a recursive sequence, there can be a finite number of undefined terms, more than... 02.04.04 to map (aver)
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Establish a set of values ​​that have a definite correspondence with quantities or values ​​in another set. Example: Calculate the value of a mathematical function, that is, for the allowed set of values ​​of the directly involved independent variables, find the value of its dependent variable.
02.04.05 map
A set of values ​​that have a definite correspondence with quantities or values ​​in another set 02.04.06 generating function, generating function function is a mathematical function that, for a given sequence of functions or constants, when the mathematical function is expressed as an infinite series, the coefficients of the series terms are the functions or constants in the given sequence. Example: The function (1-2uα+u2) is a generating function of the Legendre polynomial P(r), because there is an expansion: (1-2ux+u2)--
Pn(r)u\
02.04.07 Function threshold function is a binary logic function with one or more variables (its variables are not necessarily Boolean). If the value of a specific mathematical function of the variable exceeds a given threshold, the value of the switch function is 1, otherwise it is 0. Example: Threshold function
When g≤T, f(a,.a.)=0
When g>T, f(a,..an)=l
g-Wiai+...+Wha.
W, W are the positive weights of the real variables ai,,a,. T is the value. 02.05 Boolean operation
02.05.01 Boolean operation Boolean operation is an operation in which all operands and results can only take two values. Note: In order to simplify the definitions of various Boolean operations and the tables in the appendix, the two Boolean values ​​can be recorded as "Boolean value 0\ and "Boolean value 1". Of course, other pairs of values ​​can also be used, which does not contradict the definition. 02.05.02 Boolean operation An operation that follows the rules of Boolean algebra.
02.05.03 Dyadic Boolean operation A Boolean operation that has two and only one [N and only N] operands. 02.05.04 Boolean operator An operator whose operands and result are either of two values. 02.05.05
The complement of a Boolean operation is another Boolean operation that, when operated on with the operands of the first, produces the "inverse" of the result of the first. Example: disjunction is the complement of non-disjunction.
02.05.06 Dual operation The dual operation of a Boolean operation is another Boolean operation that, when operated on the inverse of each of its operands, produces the inverse of the result of the first. Example: disjunction is the dual operation of conjunction.
02.05.07 Identity operatian A Boolean operation that produces a Boolean result if and only if all of its operands have the same Boolean value. Note: An operation where the two operands are identical is an equivalence operation. 02.05.08 A Boolean operation where the result is the Boolean value 1 if and only if all operands have different Boolean values. 27
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Note: An operation where the two operands are not identical is a non-equivalence operation. equivalence operation, IF-AND-ONIY--{F operation02. 05. 09
A binary Boolean operation where the result is the Boolean value 1 if and only if all operands have different Boolean values. Note: See the Boolean operation table in the appendix. non-equivalence operation, EXCLUSIVE-OR oporation02.05.10 "Non-equivalence" operation, "XOR" operation A binary Boolean operation whose result is Boolean value 1 if and only if the two operands have different Boolean values. Note: See the Boolean operation table in the appendix
02. 05.11
Conjunction, "AND" operation, "INTERSECTION" conjunction, AND operation, intersection A Boolean operation whose result is Boolean value 1 if and only if all operands have Boolean value 1. Note: See the Boolean operation table in the appendix. 2 Non-conjunction, "NAND" non-conjunction, NAND operation. NOTBOIH operation02.05.12
A Boolean operation whose result is Boolean value 0 if and only if each operand has Boolean value 1. Note: See the Boolean operation table in the appendix. 02.05.13 disjunction, OR operation, INCLUSIVF-OR opcration, logicaladd
-A Boolean operation whose result is Boolean value 0 if and only if each of its operands has Boolean value 0. Note: See the table of Boolean operations in the Appendix. 02.05.14 non-disjunction, NOR operation, NEITHER-NOR operation-A binary Boolean operation whose result is Boolean value 1 if and only if each of its operands has Boolean value 0. Note: See the table of Boolean operations in the Appendix. 02.05.15 exclusion NOT-IF-THEN operation-A binary Boolean operation whose result is Boolean value 1 if and only if the first operand has Boolean value 1 and the second operand has Boolean value 0.
Note: See the table of Boolean operations in the Appendix. implication, IF-THEN operation, conditional implication (operation) 02.05.16
A binary Boolean operation whose result is Boolean value 0 if and only if the first operand has Boolean value 1 and the second operand has Boolean value 0.
Note: See the table of Boolean operations in the Appendix. 02.05.17
negation, NOT operation-A binary Boolean operation whose result is the opposite of the Boolean values ​​of its operands. Note: See the table of Boolean operations in the Appendix. 02.05.18to negate
Perform the "negation" operation.
02.06Precision, Accuracy, and Error
Precisionprecision
02. 06.01
A measure of the ability to distinguish between nearly equal values. Example: a 4-digit number is less precise than a 6-digit number, but a properly calculated 4-digit number can be more accurate than an improperly calculated 6-digit number.
02.06.02. multiple-precision multiple-precision The property of using two or more computer words to represent a number in order to increase accuracy. 02.06.03 single-[double-Etriple-]precision The property of using one [two-three] computer word to represent a number, depending on the required accuracy. 02.06.04
error
The deviation of a calculated, observed, measured value, or state from the true, given, or theoretically correct value or state. 02.06.05
accuracy
The property of being free from error.
02.06.06 Accuracy
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A qualitative estimate of the degree of error-freeness. The higher the estimate, the smaller the corresponding error. Accuracy
A quantitative measure of the size of the error, usually expressed as a relative error function. The higher the value of the measure, the smaller the corresponding error.
02.06.08 Absolute errorabsolute errorThe algebraic result obtained by subtracting the true value, given value or theoretically correct value from the calculated value, observed value, measured value or obtained value. 02.06. 09
Relative errorrelativeerror
The ratio of the absolute error to the true value, given value or theoretically correct value. 02.06.10 Balanced errorbalanced errorThe set of errors whose average value is zero.
Bias
The systematic deviation of a value from a reference value. Bias error
02. 06. 12
Error due to bias.
Example 1: Error due to shortening of a measuring ruler. Example 2: Error due to truncation in calculations. 02.06.13 Error range
The set of possible values ​​for an error.
02. 06. 14
Error span
The difference between the maximum and minimum values ​​of an error. 02.06.15 Truncation error Error due to truncation.
Rounding error
02.06. 16*
Error due to rounding.
02.07 Arithmetic
02.07.01 Binary arithmetic operation A type of arithmetic operation in which both the operands and the result are represented in pure binary. Significant digit arithmetic02. 07. 02
A method of performing calculations using modified floating point representation in which the number of significant digits of each operand is known and the number of significant digits of the result is determined by the number of significant digits of the operands and the degree of precision that can be provided.
(arithmetic) overflow02. 07. 03
The phenomenon in which the result of an arithmetic operation exceeds the word length specified by the representation of the number. 02.07.04 Overflow
The phenomenon in which the word length of the result of an operation exceeds the storage capacity of the specified storage device. 5 (arithmetic) underflow02. 07. 05
In arithmetic operations, the absolute value of the result is too small to be represented within the range of the number system used. Example 1: When the absolute value of the result is less than the smallest non-zero value that can be represented, especially when using a floating point representation system, an underflow will occur.
Example 2: The result of an operation will also underflow due to a negative exponent that exceeds the allowed range. 29
scarry digit
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When the sum or product of a digit exceeds the maximum number that can be represented by that digit, the number generated and transmitted to another place for processing.
Note: In the bitwise representation system, the carry digit is transmitted to the digit with the next higher power for processing. 02.07.07carry
The action of transmitting the carry digit.
02.07.08 to carry
The act of transferring a carry digit from the most significant digit to the least significant digit. Example: When two negative numbers represented in the two's complement representation are added, there is a carry digit. 02.07.10
borrowdigit
The digit generated when the difference between two digits is arithmetic negative and transferred to another place for processing. Note: In the bitwise representation system, the borrow digit is transferred to the higher-order digit for processing. end-around borrow
The act of transferring a borrow digit from the most significant digit to the least significant digit. 02.08 Operator Notation in Mathematics
02.08.01 Infix notation A method of forming mathematical expressions that is governed by operator precedence rules and uses paired delimiters such as parentheses. In the expression, operators are interspersed between operands, and each operator specifies the operation to be performed on the adjacent operands or intermediate results.
Example 1: The sum of A plus B multiplied by C can be expressed by the expression (A+B)×C. Example 2: The result of P and Q\ and \R is "ANDed" by the expression P&(Q&R). 02.08.02 Prefix notation, Polish notation, parenthesis-free notation A method of forming mathematical expressions in which each operator is placed in front of its operand and specifies the operation to be performed on the adjacent operands or intermediate results. Example 1: The sum of A+B multiplied by C can be expressed by the expression ×+ABC. Example 2: P and Q are ANDed with the result of \R, which can be expressed by the expression &P&.QR. 02.08.03 Postfix notation, reverse polish notation A method of forming mathematical expressions in which each operator is placed after its operand and specifies the operation to be performed on the preceding operand or intermediate result. Example 1: The sum of A plus B multiplied by C can be expressed by the expression AB+C×Example 2 P and Q are ANDed with the result of \R, which can be expressed by the expression PQR&&. 02.09 Number and quantity processing
normalize (in a floating-point representation system) to02.09.01
standardizc
In a floating-point representation, adjust the fixed-point portion and the order accordingly so that the fixed-point portion is within a specified range, while the value of the real number represented remains unchanged.
Example: If the fixed-point part is specified to be in the range of 1 to 9.99, the floating-point representation of 123.45×10 can be normalized to 1.2345X101.
02.09.02 Truncation (of a string) Delete or omit the front or back of a string according to the given criteria. 02.09.03 Truncation (of a computation process) 30
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Before a computation process reaches its final result or naturally ends (if any), terminate the process according to the given rules.
02.09.04 to round
to round
In bitwise representation, the least significant digit or digits are deleted or omitted, and the remaining part is adjusted according to a given rule.
Note: ① The purpose of rounding is usually to limit the precision of the number or to reduce the number of characters, or both. ② The most common forms of rounding in arithmetic are rounding down, rounding up, and rounding off. 02.09.05 to round down
To round down only the remaining part without adjusting it. Example: When rounded down to two decimal places with -1, the numbers 12.6317 and 15.0625 become 12.63 and 15.06 respectively. Note: () When a number is rounded down, its absolute value does not increase. ②) Rounding down is a form of truncation. 02.09.06 to round up
A form of rounding in which the least significant digit of the remaining digit is incremented by 1 and necessary carries are performed if and only if one or more non-zero digits are discarded.
Example: When rounded up to two decimal places, the numbers 12.6374 and 15.0625 are 12.64 and 15.07, respectively. Note: When a number is rounded up, its absolute value is not reduced. 02.09.07 to round off
A form of rounding in which the least significant digit of the remaining digit is incremented by 1 and necessary carries are performed if and only if the most significant digit of the number discarded is greater than or equal to -1/2 the cardinality of the digit. Example: When rounded to two decimal places, the numbers 12.6375 and 15.0625 are 12.64 and 15.0602.09.08 respectively. To round off A form of rounding that adds 1 to the least significant digit of the remaining part of the number and performs the necessary carry when one of the following conditions is encountered:
The most significant digit of the omitted part is greater than half of the cardinality of the digit; b. The most significant digit of the omitted part is equal to half of the cardinality, and at least one of the remaining omitted digits is greater than zero;
c. The most significant digit of the omitted part is equal to half of the cardinality, and the remaining digits are all equal to zero, but the least significant digit of the remaining digit is an odd number.
Example: When rounded to three decimal places, the numbers 12.6375 and 15.0625 are 12.638 and 15.062 respectively. Note: Odd numbers may also be replaced by even numbers in this definition. to scale
02. 09. 09
To express a quantity in terms of another unit of measurement so that its value fits within a given range. 02.09-10 scale factor, scaling facton A number used as a multiplier in scaling.
Example: A scaling factor of 1/1000 is suitable for compressing the values ​​856, 432, -95, and 182 into the range 1 to +1. 02.09.11 to quantize
To divide the range of a variable into a finite number of non-overlapping intervals (not necessarily of equal width) and to assign a value to each interval to identify that interval.
Example: For many purposes, the age of a person is often quantified in intervals of one year. 02.09.12 To sample
To obtain the corresponding values ​​of a function at regular or irregular intervals according to different values ​​of the independent variable within the domain of the function. Note: In other fields (such as statistics), this term may have other meanings. 31
02.10 Operation
02.10.01 Operation
operation
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A completely well-defined action that produces a new object when it is applied to any permitted combination of several known objects. Example: In the addition process in arithmetic operations, 5 and 3 are added to get 8. 5 and 3 are both operands, 8 is the result, and the addition sign is the operator, which indicates that addition is to be performed.
02.10.02 Operand operand The object involved in the operation.
02. 10.03 result result
The object produced by the completion of an operation.
02.10.04 monadic operation, unary operation An operation performed on one and only one operand. Example: "negation".
Dyadic [N-adic] operation An operation performed on two and only two [on N and only N] operands. 02.10.06 operator (in symbols manipulation) operator (in symbols manipulation) A symbol that represents the action to be performed in an operation. 02.10.07
.monadic [dyadic] operator, unary [binary] operator represents an operator that operates on one and only one [on two and only two] operands. 02.10.08
3 logical operationlogic operation, logical operationan operation performed according to the rules of symbolic logic.
9 logical operationlogic operation, logical operation02.10.09
an operation in which each character of the result depends only on the corresponding character of each operand. Example: the binary Boolean operation given in the "result" column of Appendix A.threshold operation
an operation that evaluates a threshold function of its operands.
majority operationmajerityoperatin02.10.11
an operation in which each operand can take on the value 0 or 1 and in which the value of the operation is 1 only if the number of operands that are 1 exceeds the number of operands that are 0.02.10.12to compare
an operation in which two items are tested to determine their relative size, their relative position in a sequence, or whether they have some characteristic in common.
Logical comparison
Tests two character strings to determine if they are identical. 02.11 Shift
02.11.01 Shift
Moves some or all of the characters of a word the same number of character positions toward the end of the word. 02.11.02 Arithmetic shift A shift that applies to numbers in fixed-radix number systems and numbers in fixed-point representation by moving only the characters of the fixed-point portion of the number.
Note: ① An arithmetic shift, if not affected by rounding, is usually equal to multiplying the radix by a positive or negative integer power. ② Compare logical shift with arithmetic shift, especially in floating-point representation. 02.11.03 Logical shift, logic shift A shift that treats all characters of a computer word the same. 32
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02.11.04 End-around shift, cyclic shift - a logical shift in which characters are shifted out of one end of a register or computer word and then shifted in from the other end. 02.12 Tables and diagrams
operation table
02.12.01 Operation table
A table used to define an operation. The table lists all appropriate combinations of operands and lists the results of the operation for each combination.
02.12.02 Boolean operation table A table in which each operand and result can take only one of two values. 02.12.03
truth table
A table of logical operations.
Venn diagram
A diagram that represents a set using an area drawn on a plane. Veitch diagram
A method of representing Boolean functions using rectangular diagrams in which the number of variables determines the number of squares in the diagram. The number of squares required is the number of possible states, which is the number of variables raised to the power of 2. 02.12.06 Karnaugh map
A rectangular diagram representing the logic function of a variable, the rectangular diagram is drawn with overlapping sub-rectangles, each square of these sub-rectangles represents a unique combination of logical variables, and there is an intersection to represent it for all possible combinations. 33
Corresponding complement operation
Operation result
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Appendix A
Unary Boolean operation table
(reference)
Constant value.
“Inverse”
Constant value 0
Constant value 1, constant value 1
Note: The circle represents the variable P, and the shaded part represents the defined set. 34
Example of method
Symbol representation
Venn diagram representation
Entry number
Corresponding supplementary operation
Calculation sequence number
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Appendix B
Binary Boolean Operation Table
(Reference)
Constant value 0
(First) variable
Constant value 0
P excludes Q
Excludes|Q excludes P
(Second) variable
Non-equivalence
Non-disjunction
“Equivalence”
(First) variable
“Opposite” of variable
Not P or Q
Neither P
Nor Q
P is equivalent to Q
Q implies P
Example of representationwww.bzxz.net
Fun representation
Venn diagram representation
Term number
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