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Redundant Binary Representation
A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary Numerical digit, digit so that most numbers have several representations. An RBR is unlike usual binary numeral systems, including two's complement, which use a single bit for each digit. Many of an RBR's properties differ from those of regular binary representation systems. Most importantly, an RBR allows addition without using a typical carry. When compared to non-redundant representation, an RBR makes bitwise operation, bitwise logical operation slower, but arithmetic operation#Arithmetic operations, arithmetic operations are faster when a greater bit width is used. Usually, each digit has its own sign that is not necessarily the same as the sign of the number represented. When digits have signs, that RBR is also a signed-digit representation. Conversion from RBR An RBR is a positional notation, place-value notation system. In an RBR, Numerical digit, digits ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numeral System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using Numerical digit, digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal numeral system (used in common life), the number ''three'' in the binary numeral system (used in computers), and the number ''two'' in the unary numeral system (e.g. used in Tally marks, tallying scores). The number the numeral represents is called its value. Not all number systems can represent all numbers that are considered in the modern days; for example, Roman numerals have no zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or at least a standard representation) *Reflec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Disjunction
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S , assuming that R abbreviates "it is raining" and S abbreviates "it is snowing". In classical logic, disjunction is given a truth functional semantics according to which a formula \phi \lor \psi is true unless both \phi and \psi are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AND Gate
The AND gate is a basic digital logic gate that implements logical conjunction (∧) from mathematical logic AND gate behaves according to the truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If not all inputs to the AND gate are HIGH, LOW output results. The function can be extended to any number of inputs. Symbols There are three symbols for AND gates: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated DIN symbol. Additional inputs can be added as needed. For more information see Logic gate symbols article. It can also be denoted as symbol "^" or "&". The AND gate with inputs ''A'' and ''B'' and output ''C'' implements the logical expression C = A \cdot B. This expression also may be denoted as C=A \wedge B or C=A \And B. Implementations An AND gate can be designed using only N-channel (pictured) or P-channel MOSFETs, but is usually implemented with both (CMOS). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Booth Encoding
Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London. Booth's algorithm is of interest in the study of computer architecture. The algorithm Booth's algorithm examines adjacent pairs of bits of the 'N'-bit multiplier ''Y'' in signed two's complement representation, including an implicit bit below the least significant bit, ''y''−1 = 0. For each bit ''y''''i'', for ''i'' running from 0 to ''N'' − 1, the bits ''y''''i'' and ''y''''i''−1 are considered. Where these two bits are equal, the product accumulator ''P'' is left unchanged. Where ''y''''i'' = 0 and ''y''''i''−1 = 1, the multiplicand times 2''i'' is added to ''P''; and where ''y''i = 1 and ''y''i−1 = 0, the multiplicand times 2''i'' is subtracted from ''P''. The final value of ''P'' is the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardware Multiplier
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic techniques can be used to implement a digital multiplier. Most techniques involve computing the set of ''partial products,'' which are then summed together using binary adders. This process is similar to long multiplication, except that it uses a base-2 (binary) numeral system. History Between 1947 and 1949 Arthur Alec Robinson worked for English Electric Ltd, as a student apprentice, and then as a development engineer. Crucially during this period he studied for a PhD degree at the University of Manchester, where he worked on the design of the hardware multiplier for the early Mark 1 computer. However, until the late 1970s, most minicomputers did not have a multiply instruction, and so programmers used a "multiply routine" which repeatedly shifts and accumulates partial results, often written using loop unwinding. Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operand
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above example, '+' is the symbol for the operation called addition. The operand '3' is one of the inputs (quantities) followed by the addition operator, and the operand '6' is the other input necessary for the operation. The result of the operation is 9. (The number '9' is also called the sum of the augend 3 and the addend 6.) An operand, then, is also referred to as "one of the inputs (quantities) for an operation". Notation Expressions as operands Operands may be complex, and may consist of expressions also made up of operators with operands. :(3 + 5) \times 2 In the above expression '(3 + 5)' is the first operand for the multiplication operator and '2' the second. The operand '(3 + 5)' is an expression in itself, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Logic Unit
In computing, an arithmetic logic unit (ALU) is a Combinational logic, combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs). The inputs to an ALU are the data to be operated on, called operands, and a code indicating the operation to be performed; the ALU's output is the result of the performed operation. In many designs, the ALU also has status inputs or outputs, or both, which convey information about a previous operation or the current operation, respectively, between the ALU and external status registers. Signals An ALU has a variety of input and output net (electronics), nets, which are the electrical conductors used to convey Digital signal (electronics), digi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
−1
In mathematics, −1 (also known as negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0. Algebraic properties Multiplying a number by −1 is equivalent to changing the sign of the number – that is, for any we have . This can be proved using the distributive law and the axiom that 1 is the multiplicative identity: :. Here we have used the fact that any number times 0 equals 0, which follows by cancellation from the equation :. In other words, :, so is the additive inverse of , i.e. , as was to be shown. Square of −1 The square of −1, i.e. −1 multiplied by −1, equals 1. As a consequence, a product of two negative numbers is positive. For an algebraic proof of this result, start with the equation :. The first equality follows from the above result, and the second follows from the defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive Inverse
In mathematics, the additive inverse of a number is the number that, when added to , yields zero. This number is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself. The additive inverse of is denoted by unary minus: (see also below). For example, the additive inverse of 7 is −7, because , and the additive inverse of −0.3 is 0.3, because . Similarly, the additive inverse of is which can be simplified to . The additive inverse of is , because . The additive inverse is defined as its inverse element under the binary operation of addition (see also below), which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, double additive inverse has no net effect: . Common examples For a number (and m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
