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Serial Adder
The serial binary adder or bit-serial adder is a digital circuit that performs binary addition bit by bit. The serial full adder has three single-bit inputs for the numbers to be added and the carry in. There are two single-bit outputs for the sum and carry out. The carry-in signal is the previously calculated carry-out signal. The addition is performed by adding each bit, lowest to highest, one per clock cycle. Serial binary addition Serial binary addition is done by a flip-flop and a full adder. The flip-flop takes the carry-out signal on each clock cycle and provides its value as the carry-in signal on the next clock cycle. After all of the bits of the input operands have arrived, all of the bits of the sum have come out of the sum output. Serial binary subtracter The serial binary subtracter operates the same as the serial binary adder, except the subtracted number is converted to its two's complement before being added. Alternatively, the number to be subtracted is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Circuit
In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates they contain and the values the gates can produce. For example, the values in a Boolean circuit are boolean values, and the circuit includes conjunction, disjunction, and negation gates. The values in an integer circuit are sets of integers and the gates compute set union, set intersection, and set complement, as well as the arithmetic operations addition and multiplication. Formal definition A circuit is a triple (M, L, G), where * M is a set of values, * L is a set of gate labels, each of which is a function from M^ to M for some non-negative integer i (where i represents the number of inputs to the gate), and * G is a labelled directed acyclic graph with labels fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Adder
Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that takes two arguments * Binary relation, a relation involving two elements * Binary-coded decimal, a method for encoding for decimal digits in binary sequences * Finger binary, a system for counting in binary numbers on the fingers of human hands Computing * Binary code, the digital representation of text and data * Bit, or binary digit, the basic unit of information in computers * Binary file, composed of something other than human-readable text ** Executable, a type of binary file that contains machine code for the computer to execute * Binary tree, a computer tree data structure in which each node has at most two children Astronomy * Binary star, a star system with two stars in it * Binary planet, two planetary bodies of comparable ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full Adder
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. Binary adders Half adder The half adder adds two single binary digits ''A'' and ''B''. It has two outputs, sum (''S'') and carry (''C''). The carry signal represents an overflow into the next digit of a multi-digit addition. The value of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flip-flop (electronics)
In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems. Flip-flops and latches are used as data storage elements. A flip-flop is a device which stores a single ''bit'' (binary digit) of data; one of its two states represents a "one" and the other represents a "zero". Such data storage can be used for storage of ''state'', and such a circuit is described as sequential logic in electronics. When used in a finite-state machine, the output and next state depend not only on its current input, but also on its current state (and hence, previous inputs). It can also b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subtracter (electronics)
In electronics, a subtractor – a digital circuit that performs subtraction of numbers – can be designed using the same approach as that of an adder. The binary subtraction process is summarized below. As with an adder, in the general case of calculations on multi-bit numbers, three bits are involved in performing the subtraction for each bit of the difference: the minuend (X_), subtrahend (Y_), and a borrow in from the previous (less significant) bit order position (B_). The outputs are the difference bit (D_) and borrow bit B_. The subtractor is best understood by considering that the subtrahend and both borrow bits have negative weights, whereas the X and D bits are positive. The operation performed by the subtractor is to rewrite X_-Y_-B_ (which can take the values -2, -1, 0, or 1) as the sum -2B_+D_. : D_ = X_ \oplus Y_ \oplus B_ : B_ = X_ < (Y_ + B_) Subtractors are usually implemented within a binary adder for only a small cost when using the standard |
Two's Complement
Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian numbers, rightmost bit in little-endian numbers) to indicate whether the binary number is positive or negative (the sign). It is used in computer science as the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. When the most significant bit is a one, the number is signed as negative. . Two's complement is executed by 1) inverting (i.e. flipping) all bits, then 2) adding a place value of 1 to the inverted number. For example, say the number −6 is of interest. +6 in binary is 0110 (the leftmost most significant bit is needed for the sign; positive 6 is not 110 because it would be interpreted as -2). Step one is to flip all bits, yielding 1001. St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ones' Complement
The ones' complement of a binary number is the value obtained by inverting all the bits in the binary representation of the number (swapping 0s and 1s). The name "ones' complement" (''note this is possessive of the plural "ones", not of a singular "one"'') refers to the fact that such an inverted value, if added to the original, would always produce an 'all ones' number (the term "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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Binary Adder
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. Binary adders Half adder The half adder adds two single binary digits ''A'' and ''B''. It has two outputs, sum (''S'') and carry (''C''). The carry signal represents an overflow into the next digit of a multi-digit addition. The value of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Arithmetic
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
