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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, ones' complement, or two's complement operations. This allows the calculator to emulate the programmer's c ...
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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, 2023–present). *#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 e ...
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Hexadecimal
Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen. Software developers and system designers widely use hexadecimal numbers because they provide a convenient representation of binary code, binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble). For example, an 8-bit byte is two hexadecimal digits and its value can be written as to in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value would be expressed in hexadecimal as . In programming, several notations denote hexadecimal numbers, usually involving a prefi ...
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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 prefix or Polish notation (PN), in which operators ''precede'' their operands. The notation does not need any parentheses for as long as each operator has a fixed number of operands. The term ''postfix notation'' describes the general scheme in mathematics and computer sciences, whereas the term ''reverse Polish notation'' typically refers specifically to the method used to enter calculations into hardware or software calculators, which often have additional side effects and implications depending on the actual implementation involving a stack. 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 G ...
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Programmable Calculator
Programmable calculators are calculators that can automatically carry out a sequence of operations under the 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 for 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 manufacturer ...
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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 signif ...
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Ones' Complement
The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the Binary number, binary representation of the number. The name "ones' complement" refers to the fact that such an inverted value, if added to the original, would always produce an "all ones" number (the term "Method of complements, complement" refers to such pairs of mutually additive inverse numbers, here in respect to a non-0 base number). This mathematical operation is primarily of interest in computer science, where it has varying effects depending on how a specific computer represents numbers. A ones' complement system or ones' complement arithmetic is a system in which negative numbers are represented by the inverse of the binary representations of their corresponding positive numbers. In such a system, a number is negated (converted from positive to negative or vice versa) by computing its ones' complement. An N-bit ones' complement numeral system can only represent int ...
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Two's Complement
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''sign'' to indicate whether the binary number is positive or negative; when the most significant bit is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the bitwise NOT operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary. Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers and differ only in the integer overflow situations. Proce ...
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Bit Shifting
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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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, 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 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 bitwise OR operation can be used, following the principle that for an individual bit Y, 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 (bits 0, 1, 2, 3) unchanged. 10010101 10100101 OR 11110000 11110000 = 11110101 1111 ...
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Word Size
In computing, a word is any processor design's natural unit of data. 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 rather than bytes ...
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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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