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HP-16C
The HP-16C Computer Scientist is a programmable pocket calculator that was produced by Hewlett-Packard between 1982 and 1989. It was specifically designed for use by computer programmers, to assist in debugging. It is a member of the HP Voyager series of programmable calculators. It was the only programmer's calculator ever produced by HP, though many later HP calculators have incorporated most of the 16C's functions. Features The 16C can display integers in hexadecimal, decimal, octal and binary, and convert numbers from one number base to another. It also deals with floating-point decimal numbers. To accommodate long integers, the display can be 'windowed' by shifting it left and right. For consistency with the computer the programmer is working with, the word size can be set to different values from 1 to 64 bits. Binary-arithmetic operations can be performed as unsigned, one's complement, or two's complement operations. This allows the calculator to emulate the programmer's co ...
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HP Voyager Series
The Hewlett-Packard Voyager series of calculators were introduced by Hewlett-Packard in 1981. All members of this series are Programmable calculator, programmable, use Reverse Polish Notation, and feature HP Continuous memory, continuous memory. Nearly identical in appearance, each model provided different capabilities and was aimed at different user markets. Models The HP calculators Voyager series consisted of five models, some of which were manufactured in several variants (with years of production): *#10C, HP-10C – basic scientific calculator (1982–1984). *#11C, HP-11C – mid-range scientific calculator (1981–1989). *#12C, HP-12C – business/financial calculator (1981–present). *#15C, HP-15C – advanced scientific calculator (1982–1989, 2011). *#16C, HP-16C – computer programmer's calculator (1982–1989). HP-10C The HP-10C is the last and lowest-featured calculator in this line, even though its number would suggest an earlier origin. T ...
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Reverse Polish Notation
Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators ''follow'' their operands, in contrast to Polish notation (PN), in which operators ''precede'' their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924. The first computer to use postfix notation, though it long remained essentially unknown outside of Germany, was Konrad Zuse's Z3 in 1941 as well as his Z4 in 1945. The reverse Polish scheme was again proposed in 1954 by Arthur Burks, Don Warren, and Jesse Wright and was independently reinvented by Friedrich L. Bauer and Edsger W. Dijkstra in the early 1960s to reduce computer memory access and use the stack to evaluate expressions. The algorithms and notation for this scheme were extended ...
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Programmable Calculator
Programmable calculators are calculators that can automatically carry out a sequence of operations under control of a stored computer programming, program. Most are Turing complete, and, as such, are theoretically general-purpose computers. However, their user interfaces and programming environments are specifically tailored to make performing small-scale numerical computations convenient, rather than general-purpose use. The first programmable calculators such as the IBM CPC used punched cards or other media for program storage. Hand-held electronic calculators store programs on magnetic strips, removable read-only memory cartridges, flash memory, or in battery-backed read/write memory. Since the early 1990s, most of these flexible handheld units belong to the class of graphing calculators. Before the mass-manufacture of inexpensive dot-matrix LCDs, however, programmable calculators usually featured a one-line numeric or alphanumeric display. The Big Four manufacturers of pro ...
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Word Size
In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word (the ''word size'', ''word width'', or ''word length'') is an important characteristic of any specific processor design or computer architecture. The size of a word is reflected in many aspects of a computer's structure and operation; the majority of the registers in a processor are usually word-sized and the largest datum that can be transferred to and from the working memory in a single operation is a word in many (not all) architectures. The largest possible address size, used to designate a location in memory, is typically a hardware word (here, "hardware word" means the full-sized natural word of the processor, as opposed to any other definition used). Documentation for older computers with fixed word size commonly states memory sizes in words ra ...
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Floating-point Number
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point ...
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Scientific Calculator
A scientific calculator is an electronic calculator, either desktop or handheld, designed to perform mathematical operations. They have completely replaced slide rules and are used in both educational and professional settings. In some areas of study scientific calculators have been replaced by graphing calculators and financial calculators which have the capabilities of a scientific calculator along with the capability to graph input data. Functions When scientific calculators were originally marketed they normally had only four of five capabilities (addition, subtraction, multiplication, division and square root). Modern scientific calculators generally have many more capabilities than the original four or five function calculator, and the capabilities differ between manufacturers and models. The capabilities of a modern scientific calculator include: * scientific notation * floating-point decimal arithmetic * logarithmic functions, using both base 10 and base e * t ...
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Square Root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'', which is denoted by \sqrt, where the symbol \sqrt is called the ''radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case 9. For nonnegative , the principal square root can also be written in exponent notation, as . Every positive number has two square roots: \sqrt, which is positive, and -\sqrt, which is negative. The two roots can be written more concisely using the ± sign as \plusmn\sqrt. ...
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Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a rational number, fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the Function (mathematics), function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an Involution (mathematics), involution). Multiplying by a number is the same as Division (mathematics), dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yiel ...
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Bitwise Logical Operation
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least signif ...
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Bitwise Operation
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least signi ...
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Bit Masking
In computer science, a mask or bitmask is data that is used for bitwise operations, particularly in a bit field. Using a mask, multiple bits in a byte, nibble, Word (computer architecture), word, etc. can be set either on or off, or inverted from on to off (or vice versa) in a single bitwise operation. An additional use of masking involves Predication (computer architecture), predication in vector processing, where the bitmask is used to select which element operations in the vector are to be executed (mask bit is enabled) and which are not (mask bit is clear). Common bitmask functions Masking bits to 1 To turn certain bits on, the Logical disjunction, bitwise OR operation can be used, following Logical disjunction#Bitwise operation, the principle that Y OR 1 = 1 and Y OR 0 = Y. Therefore, to make sure a bit is on, OR can be used with a 1. To leave a bit unchanged, OR is used with a 0. Example: Masking ''on'' the higher nibble (bits 4, 5, 6, 7) while leaving the lower nibble ( ...
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Bitwise Rotation
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least signi ...
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