Abstract: Systems and methods are provided to perform multiplication-delayed-addition operations in a systolic array to increase clock speeds, reduce circuit area, and/or reduce dynamic power consumption. Each processing element in the systolic array can have a pipeline configured to perform a multiplication during a first systolic interval and to perform an accumulation during a second systolic interval. The multiplication result from the first systolic interval can be stored in a delay register for use by the accumulator during the second systolic interval. A skip detection circuit can be used to skip one or more of the multiplication, storing in the delay register, and the addition during skip conditions for improved energy efficiency.

Abstract: Disclosed embodiments relate to computing dot products of nibbles in tile operands. In one example, a processor includes decode circuitry to decode a tile dot product instruction having fields for an opcode, a destination identifier to identify a M by N destination matrix, a first source identifier to identify a M by K first source matrix, and a second source identifier to identify a K by N second source matrix, each of the matrices containing doubleword elements, and execution circuitry to execute the decoded instruction to perform a flow K times for each element (M,N) of the identified destination matrix to generate eight products by multiplying each nibble of a doubleword element (M,K) of the identified first source matrix by a corresponding nibble of a doubleword element (K,N) of the identified second source matrix, and to accumulate and saturate the eight products with previous contents of the doubleword element (M,N).

Abstract: A finite impulse response (FIR) filter including a delay line and a plurality of arithmetic units. Each arithmetic unit is coupled to a different one of a plurality of tap points of the delay line, is configured to receive a respective signal value over the delay line, and is associated with a respective coefficient. Any given one of the arithmetic units is configured to receive a respective control word. The respective control word specifying: (i) a plurality of trivial multiplication operations, and (ii) a plurality of bit shift operations. Any given one of the arithmetic units is further configured to estimate or calculate a product of the respective signal of the arithmetic unit respective signal value and the respective coefficient of the arithmetic unit by performing the trivial multiplication operations and bit shift operations that are specified by the respective control word that is received at the given arithmetic unit.

Abstract: A method for implementing a multiplier on a programmable logic device (PLD) is disclosed. Partial product bits of the multiplier are identified and how the partial product bits are to be summed to generate a final product from a multiplier and multiplicand are determined. Chains of PLD cells and cells in the chains of PLD cells for generating and summing the partial product bits are assigned. It is determined whether a bit in an assigned cell in an assigned chain of PLD cells is under-utilized. In response to determining that a bit is under-utilized, the assigning of the chains of PLD cells and cells for generating and summing the partial product bits are changed to improve an overall utilization of the chains of PLD cells and cells in the chains of PLD cells.

Abstract: A processor includes a front end including circuitry to decode a first instruction to set a performance register for an execution unit and a second instruction, and an allocator including circuitry to assign the second instruction to the execution unit to execute the second instruction. The execution unit includes circuitry to select between a normal computation and an accelerated computation based on a mode field of the performance register, perform the selected computation, and select between a normal result associated with the normal computation and an accelerated result associated with the accelerated computation based on the mode field.

Abstract: A very long instruction word (VLIW) processor that performs efficient processing including extended bits operations is provided. The VLIW processor includes an instruction control unit, a register file unit, and an instruction execution unit. The instruction execution unit includes a plurality of slots, and a state register arranged between the second slot and the third slot to transfer N-bit data between the second and third slots. The VLIW processor stores data output from the third slot into the state register and uses the data, and thus achieves efficient processing including bit-expanded operations, such as processing performed in response to instructions commonly used in image processing, image recognition, and other processing, while preventing scaling up of the circuit.

Abstract: An approach is provided that collects data from a multi-function adapter that is used by multiple functions. In the approach, a master function is dynamically selected from the group of functions. The approach further allows the master function to perform a disruptive adapter data collection while inhibiting performance of disruptive adapter data collection processes by the other (non-master) functions.

Abstract: An approach is provided that collects data from a multi-function adapter that is used by multiple functions. In the approach, a master function is dynamically selected from the group of functions. The approach further allows the master function to perform a disruptive adapter data collection while inhibiting performance of disruptive adapter data collection processes by the other (non-master) functions.

Abstract: Integrated circuits such as application specific integrated circuits or programmable logic devices may include multiple copies of a same circuit together with a majority vote circuit in a configuration that is sometimes also referred to as multi-mode redundancy. An adder circuit may be coupled to these multiple copies and produce a carry-out signal and a sum signal based on signals received from the multiple copies. The carry-out signal of the adder circuit may provide the result of the majority vote operation. A logic exclusive OR gate may perform a logic exclusive OR operation between the sum signal and the carry-out signal, thereby generating an error signal. The error signal may indicate that one of the multiple copies produces an output that is different than the outputs produced by the other copies.

Abstract: An apparatus and a method for generating a partial product for a polynomial operation are provided. The apparatus includes first encoders, each of the first encoders configured to selectively generate and output one of mutually exclusive values based on two inputs. The apparatus further includes a second encoder configured to generate and output two candidate partial products based on an output from a first one of the first encoders that is provided at a reference bit position of the inputs, an output from a second one of the first encoders that is provided at an upper bit position of the inputs, and a multiplicand. The apparatus further includes a multiplexer configured to select one of the candidate partial products output from the second encoder.

Abstract: A system and method are provided for dynamically reducing power consumption of floating-point logic. A disable control signal that is based on a characteristic of a floating-point format input operand is received and a portion of a logic circuit is disabled based on the disable control signal. The logic circuit processes the floating-point format input operand to generate an output.

Abstract: A 3× circuit for partial product generation used in a radix-8 multiplier receiving only a single multiplicand input. Rather than providing 2-inputs to the adder (a 2× of multiplicand and the multiplicand itself), the new 3× circuit uses the multiplicand as the only input. Thus, in terms of connections at the multiplier circuit level, only one bus is required to connect to the input of the new 3× circuit. The 3× generation adder circuit further operates at a reduced number of logic levels and speeds up the critical path by taking advantage of the repetition and fixed spatial separation of the bits for the adder inputs.

Abstract: A multiplier circuit for generating a product of at least first and second multiplicands includes encoding circuitry comprising a plurality of encoders. Each of the encoders is operative to receive at least a subset of bits of the first multiplicand and to generate a partial product corresponding to the subset of bits of the first multiplicand. The encoding circuitry is further operative to incorporate a negation of the product as a function of at least a first control signal supplied to the multiplier circuit. The multiplier circuit further includes summation circuitry coupled with the encoding circuitry. The summation circuitry is operative to sum each of the partial products generated by the encoding circuitry to thereby generate the product without performing post-incrementation.

Abstract: An apparatus is provided for performing carryless multiplication. The apparatus has an opcode dectector and a carryless preformat unit. The opcode dectector is configured to receive a carryless multiplication instruction, and is configured to assert a carryless signal responsive to receipt of the carryless multiplication instruction. The carryless preformat unit is configured to partition the first operand into parts responsive to assertion of the carryless signal, where the parts are configured such that a Booth encoder selects first partial products corresponding to a second operand and is precluded from selection of second partial products corresponding to the second operand, and where the second partial products are results of implicit carry operations. The first partial products are exclusive-ORed together to yield a carryless multiplication result.

Abstract: An electronic multiplier, such as a multiplication circuit, may include a partial product generator, a Booth code encoder and an accumulator. The partial product generator may generate partial product data based on a Booth code and multiplicand data. The Booth code encoder may generate the Booth code based on multiplier data. The Booth code may include a zero-generation Booth code and a zero-avoidance Booth code. The Booth code encoder may selectively generate the zero-generation Booth code or the zero-avoidance Booth code when the partial product data correspond to a partial product of zero. The accumulator accumulates the partial product data to provide a multiplication result of the multiplicand data and the multiplier data.

Abstract: The digital propagate, digit generate, sum+0, and sum+1 terms used in typical carry-propagate adders are generated directly off the multiplicand. During the direct generation, the logic takes into account that each digit will be tripled and if each digit's next less significant digit is greater than 4. Using this technique, the generation of the multiplicand is significantly faster and uses less circuitry.

Abstract: A multiplier includes an operation unit that adds or subtracts a first group selected from a current input data, and a second group selected from a next input data corresponding to the first group to generate an operation result, a Booth's encoder that encodes the operation result according to Booth's algorithm, and generates code data, a partial product generation unit that calculates a partial product from the code data as a first partial product, and calculates, in a case where the first group and the second group are specific combination, a second partial product, and an adder that cumulatively adds an output from the partial product generation unit. The specific combination is a combination in which the highest-order bit of each of the first group and the second group is the same value, and the third least significant bit obtained after the subtraction operation is 1.

Abstract: A circuit structure efficiently multiplies a first and second number. The circuit structure includes multipliers for the pairs of three-bit digits of the first number and three-bit digits of the second number. The multipliers produce six-bit partial products from the pair of three-bit digits of the first and second numbers. Each multiplier includes look-up tables receiving the pair of three-bit digits of the first and second numbers. A summing-tree circuit includes adders arranged in a series of levels, the adders in an initial one of the levels producing partial sums from the six-bit partial products from the multipliers, and for each first and successive second ones of the levels in the series, the adders in the second level producing another plurality of partial sums from the partial sums from the first level. A last one of the levels includes the adder that produces a product of the first and second numbers.

Abstract: Multiplication engines and multiplication methods are provided. A multiplication engine for a digital processor includes a first multiplier to generate unequally weighted partial products from input operands in a first multiplier mode; a second multiplier to generate equally weighted partial products from input operands in a second multiplier mode; a multiplexer to select the unequally weighted partial products in the first multiplier mode and to select the equally weighted partial products in the second multiplier mode; and a carry save adder array configured to combine the selected partial products in the first multiplier mode and in the second multiplier mode.

Abstract: A multiplier circuit comprises a fused Booth encoder multiplexer which produces partial product bits, a tree which uses the partial product bits to generate partial products, and an adder which uses the partial products to generate intermediate sum and carry results for a multiplication operation. The fused Booth encoder multiplexer utilizes encoder-selector cells having a logic tree which carries out a Boolean function according to a Booth encoding and selection algorithm to produce one of the partial product bits at a dynamic node, and a latch connected to the dynamic node which maintains the value at an output node. The encoder-selector cells operate in parallel to produce the partial product bits generally simultaneously. A given one of the encoder-selector cells has a unique set of both multiplier operand inputs and multiplicand operand inputs, and produces a single partial product bit.

Abstract: The present invention provides processing systems, apparatuses, and methods that support both general processing processor (GPP) and digital signal processor (DSP) features, such as vector and single value multiplication. In an embodiment, fractional arithmetic, integer arithmetic, saturation, and single instruction multiple data (SIMD) operations such as vector multiply, multiply accumulate, dot-product accumulate, and multiply-subtract accumulate are supported. In an embodiment, the process core and/or multiplier multiplies vector values or single values by creating partial products for each desired product. These partial products are added to produce intermediate results, which are combined in different ways to support various GPP and DSP operations.

Abstract: Some embodiments provide a method of performing a mathematical operation on a set of operands. The mathematical operation includes several sub-operations. The method examines several bits of at least one operand at a time and depending on the value of these bits, reconfigures a single logic circuit to perform one of the sub-operations to generate a partial result of the mathematical operation. In some embodiments, the logic circuit is reconfigured by receiving a first set of configuration data that cause the logic circuit to reconfigure to perform a first sub-operation operation and a second set of configuration data that cause the logic circuit to reconfigure to perform a second sub-operation. In some embodiments, the logic circuit receives different inputs based on the value of the bits being examined. In some embodiments, the mathematical operation is multiplication and the sub-operations are addition and subtraction.

Abstract: A pre-saturating multiplier inspects the operands to a multiply operation prior to performing any multiplication. If the operands will cause an overflow requiring saturation, the multiplier outputs the saturated value without multiplying the original operands. In one embodiment, parameters derived from the operands are altered such that when the multiply operation is performed on the altered parameters, the multiplier produces the saturated result. This may comprise altering a Booth recoded bit group to select a negative zero instead of a zero as a partial product, and suppressing the addition of the value one to the partial products (thus effectively subtracting the value one). In another embodiment, when the operands that will cause an overflow are detected, the output of the multiplier is forced to a predetermined saturation value.

Abstract: For one disclosed embodiment, an apparatus comprises first circuitry to output encoded data from an addressable location based at least in part on an address corresponding to a first number, wherein the encoded data is based at least in part on data that corresponds to the first number and that is encoded for partial product reduction, and second circuitry to generate a product based at least in part on the encoded data and on data corresponding to a second number. Other embodiments are also disclosed.

Abstract: Methods and apparatus for converting a radix 2 multiplier to respective groups of radix 4 encoded bits representing numbers of the group consisting of ?2, ?1, 0, 1, 2, wherein the set of encoded bits includes: a first bit that is true when the associated number is 2, a second bit that is true when the associated number is ?2, a third bit that is true when the associated number is either negative or zero, and a fourth bit that is true when the associated number has an absolute value of 1.

Abstract: Techniques for the design and use of a digital signal processor, including processing transmissions in a communications (e.g., CDMA) system. A modified Booth multiplication system and process determine a multiplicand, A, and a multiplier, B. Radix-m, (e.g., radix-4) Booth recoding on B generates “n” multiplication factors, where “n,” an integer, is approximating one half of the number of the multiplier bits. “n” partial products are generated using the “n” multiplication factors as multipliers of A. Then, a multiplication tree is formed using radix-m Booth encoding. The multiplication tree includes multiplier bits associated to generate a multiplication factors. In the event of a negative multiplication factor, a two's complement of A is formed by inverting the bits of A and associating a sticky “1” to complete the two's complementation. Furthermore, multiplication factors are reduced in multiple stages to a form sum and carry components of a pre-determined length.

Abstract: A Booth decoder may comprise three circuits that run in parallel. A first circuit is used to generate a shift control signal output. A second circuit is used to generate a zero control signal output. A third circuit is used to generate an invert control signal output. The first and second circuits receive the three-bit block as an input and generate their respective outputs based on the setting of each of the bits. The third circuit receives only the most significant bit of the three-bit block as its input and generates an invert signal output based on the setting of the most significant bit. In each of these circuits, the number of complex gates and transistors is minimized thereby reducing gate delay and power consumption in generating the control signals for performing a Booth multiplication operation.

Abstract: Techniques for the design and use of a digital signal processor, including processing transmissions in a communications (e.g., code division multiple access) system. Power-efficient sign extension for Booth multiplication processes involves applying a sign bit in a Booth multiplication tree. The sign bit allows the Booth multiplication process to perform a sign extension step. This further involves one-extending a predetermined partial product row of the Booth multiplication tree using a sign bit for preserving the correct sign of the predetermined partial product row. The process and system resolve the signal value of the sign bit by generating a sign-extension bit in the Booth multiplication tree. The sign-extension bit is positioned in a carry-out column to extend the product of the Booth multiplication process.

Abstract: A design structure for a Booth decoder is provided. The Booth decoder may comprise three circuits that run in parallel. A first circuit is used to generate a shift control signal output. A second circuit is used to generate a zero control signal output. A third circuit is used to generate an invert control signal output. The first and second circuits receive the three-bit block as an input and generate their respective outputs based on the setting of each of the bits. The third circuit receives only the most significant bit of the three-bit block as its input and generates an invert signal output based on the setting of the most significant bit. In each of these circuits, the number of complex gates and transistors is minimized thereby reducing gate delay and power consumption in generating the control signals for performing a Booth multiplication operation.

Abstract: A multiplier includes an operation unit that adds or subtracts a first group selected from a current input data, and a second group selected from a next input data corresponding to the first group to generate an operation result, a Booth's encoder that encodes the operation result according to Booth's algorithm, and generates code data, a partial product generation unit that calculates a partial product from the code data as a first partial product, and calculates, in a case where the first group and the second group are specific combination, a second partial product, and an adder that cumulatively adds an output from the partial product generation unit. The specific combination is a combination in which the highest-order bit of each of the first group and the second group is the same value, and the third least significant bit obtained after the subtraction operation is 1.

Abstract: A digital signal processor architecture allows the digital signal processor to be used efficiently for multiplying words which are longer than the word length for which the architecture is primarily designed. The multiplication unit has a register file which is adapted to store data words of a first length, and a multiplier which is adapted to multiply together data words of a second length, the second length being twice the first length. In a first mode, the architecture multiplies data words of the first length, by extending them to the second length. In a second mode, the architecture multiplies data words of the second length, by retrieving each of the data words in two parts, each part being of the first length.

Abstract: An apparatus and method are disclosed for providing higher radix redundant digit lookup tables for digital lookup table circuits. A compressed direct lookup table unit accesses a redundant digits lookup table that is capable of providing a high order part and a low order part that can be directly concatenated to form an output numeric value. The redundant digits lookup table of the invention is structured so that no output overflow exceptions are created. A redundant digits lookup table recoder capable of providing recoded output values directly to partial product generators of a multiplier unit is also disclosed.

Abstract: An encoder of a multiplier may include an operator generating unit for encoding a plurality of received multiplier data to output a plurality of operators. The encoder may include a partial-product data generating unit that generates a sign selecting operator from the received multiplier data for determining signs of the operators and output paths for the multiplicand data therein prior to receiving the plurality of operators from the operator generating unit, and outputs partial-product data in response to the received plurality of operators.

Abstract: A system for multiplication of multi-bit first and second values. A processor is provided that has first and second memories with bit-positions that can all be zero or one and where the first memory has a low bit (LB). The first value is arranged in the first memory so its LSB is in the first memory LB, and the remaining bit-positions in the first memory are set to zero. The second value is arranged in the second memory such that its LSB is in the bit-position of the second memory that is next higher in order than the MSB of the first value in the first memory, and the remaining bit-positions in the second memory are set to zero. A +* operation is then performed a quantity of times equaling the number of significant bits in the first value, inclusive, thus obtaining the product of the first and second values.

Abstract: The present invention provides a system and method for improving the performance of general-purpose processors by implementing a functional unit that computes the product of a matrix operand with a vector operand, producing a vector result. The functional unit fully utilizes the entire resources of a 128b by 128b multiplier regardless of the operand size, as the number of elements of the matrix and vector operands increase as operand size is reduced. The unit performs both fixed-point and floating-point multiplications and additions with the highest-possible intermediate accuracy with modest resources.

Abstract: In an arithmetic device which performs a multiplication of a multiplicand A and a multiplier B expressed by bit patterns using a secondary Booth algorithm, an encoder selects a partial product indicating ?A when the value of i specifying three consecutive bits of B is 0, and selects a partial product indicating 0 when the value of i is not 0. An addition circuit generates a two's complement of A from the partial product indicating ?A, and outputs it as a multiplication result.

Abstract: A unified data flow is provided that allows multiplication of SIMD and non-SIMD multiplies in one multiplier. The multiplies may be both integer and floating point operations. The multiplier is partitionable having a plurality of sub-trees. The multiplier is configured to be a single tree structure in response to a non-SIMD multiplication instruction and as a partitioned tree structure in response to a SIMD multiplication instruction. At least two multiplication operations can be performed in parallel in the partitioned tree structure in response to the SIMD multiplication instruction and a single multiplication operation is performed in the single tree structure in response to the non-SIMD multiplication instruction. Appropriate formatting of the input operands and selection of data from the tree structures is performed in accordance with the instruction.

Abstract: A low-error fixed-width multiplier receives a W-bit input and produces a W-bit product. In an embodiment, a multiplier (Y) is encoded using modified Booth coding. The encoded multiplier (Y) and a multiplicand (X) are processed together to generate partial products. The partial products are accumulated to generate a product (P). To compensate for the quantization error, Booth encoder outputs are used for the generation of error compensation bias. The truncated bits are divided into two groups, a major least significant bit group and a minor least significant bit group, depending upon their effects on the quantization error. Different error compensation methods are applied to each group.

Abstract: A Booth decoder apparatus and method are provided. The Booth decoder apparatus may comprise three circuits that run in parallel. A first circuit is used to generate a shift control signal output. A second circuit is used to generate a zero control signal output. A third circuit is used to generate an invert control signal output. The first and second circuits receive the three-bit block as an input and generate their respective outputs based on the setting of each of the bits. The third circuit receives only the most significant bit of the three-bit block as its input and generates an invert signal output based on the setting of the most significant bit. In each of these circuits, the number of complex gates and transistors is minimized thereby reducing gate delay and power consumption in generating the control signals for performing a Booth multiplication operation.

Abstract: A multiplier circuit to receive a multiplier and a multiplicand comprises at least one Booth encoder circuit to encode a plurality of multiplier bits into four encoded outputs. The encoded outputs select Booth-multiply functions. The circuit also includes a plurality of multiplexer circuits, one multiplexer circuit for each bit of the multiplicand. The at least one of the plurality multiplexer circuits includes four pass gates coupled to receive a multiplicand bit, a complement of the multiplicand bit, multiplexed data from a next lower order multiplexer circuit and the encoded outputs of the Booth encoder circuit outputs to provide one bit of a partial product at a multiplexer output.

Abstract: A digital circuit including a Booth encoder having inputs for receiving a plurality of adjacent bits of a first binary input number, and an encoder control input for allowing selection between multiplication of first and second binary input numbers and multiplication of the pairs of binary numbers smaller than the first or second input number, the encoder being configured to encode the bits of the first binary input number dependent on the encoder control input to generate Booth encoded outputs for use in selection of a partial product, the Booth encoder being for use with a selector having inputs for receiving a plurality of adjacent bits of the second binary input number, and for receiving the Booth encoded outputs from the encoder, the selector being configured to select a partial product bit according to the Booth encoded outputs and the bits of the second binary input number.

Abstract: The method of locating a servo motor controller's position of the present invention utilizes accrual calculation method to ensure the positions of motor controller at each station of the production line is correctly obtained, wherein the last digit of the gear ratio is utilized to obtain a critical value so that the inputted pulse value and the gear ratio are be calculated to result a quotient and a remainder. The remainder is compared with the critical value first in order to determine the following processes of the quotient, the remainder and the last digit of gear ratio. The quotient and the remainder are stored in the quotient temporary storage device and remainder temporary storage device respectively to ensure the actual pulse value of the motor will not be cumulated with the position calculating errors.

Abstract: A multiplier circuit comprises a fused Booth encoder multiplexer which produces partial product bits, a tree which uses the partial product bits to generate partial products, and an adder which uses the partial products to generate intermediate sum and carry results for a multiplication operation. The fused Booth encoder multiplexer utilizes encoder-selector cells having a logic tree which carries out a Boolean function according to a Booth encoding and selection algorithm to produce one of the partial product bits at a dynamic node, and a latch connected to the dynamic node which maintains the value at an output node. The encoder-selector cells operate in parallel to produce the partial product bits generally simultaneously. A given one of the encoder-selector cells has a unique set of both multiplier operand inputs and multiplicand operand inputs, and produces a single partial product bit.

Abstract: A method and apparatuses for performing binary multiplication on signed and unsigned operands of various lengths is discussed herein. It is a concept that may be split into two parts, the first of which is the multiplication hardware itself, a compact, less than-full sized multiplier employing Booth or other type of recoding methods upon the multiplier to reduce the number of partial products per scan, and implemented in such a manner so that a multiplication operation with large operands may be broken into subgroups of operations that will fit into this mid-sized multiplier whose results, here called modular products, may be knitted back together to form a correct, final product. The second part of the concept is the supporting hardware used to separate the operands into subgroups and input the data and control signals to the multiplier, and the algorithms and apparatuses used to align and combine the modular products properly to obtain the final product.

Abstract: A system and method for reducing power consumption in digital circuitry by reducing the amount of unnecessary switching in such circuitry. An aspect of the present invention provides a switching-reduction circuit that outputs a signal to a subsequent digital circuit. The value of the signal may depend on the relevance of the signal value to a next output of the subsequent digital circuit. A method according to various aspects of the present invention includes receiving a next input signal. The method further includes determining whether the next input signal may be relevant to a next output of a subsequent digital circuit. The method further includes providing the next input signal to the subsequent digital circuit when the next input signal may be relevant to the next output of the subsequent digital circuit, and providing a previous signal to the subsequent digital circuit when the next input signal will not be relevant to the next output of the subsequent digital circuit.

Abstract: A multiply execution unit that is operable to generate the integer product and the XOR product of a multiplicand and a multiplier. The multiply execution unit includes a summing circuit for summing a plurality of partial products. The partial products may be Booth encoded. The summing circuit can generate an integer sum of the plurality of partial products and can generate an XOR sum of the plurality of partial products. The summing circuit includes a first plurality of full adders. The first plurality of full adders each has three inputs, a carry output, and a sum output. The sum outputs of the first plurality of full adders are independent of the value of any carry output in the summing circuit. The summing circuit also includes a second plurality of full adders. The second plurality of full adders each has three inputs, a carry output, and a sum output.

Abstract: An arithmetic unit for multiplying a first quantity x by a second quantity y, the arithmetic unit including a Booth coder having a plurality of inputs for receiving a plurality bits of the second quantity and a plurality of outputs for providing Booth coded outputs; and circuitry connected to at least one of the inputs and the outputs for modifying at least one output of the coder.

Abstract: In the multiplier, a partial product circuit generates a partial product based on a multiplicand operand and outputs of a Booth recoder circuit, which operates on a multiplier operand. The partial product circuit ANDs the multiplicand with a zero Booth recoded output, which indicates whether to zero out the multiplicand. An enable circuit selectively enables the multiplier circuit, and more particularly, disables the multiplier circuit by making the zero Booth recoded output indicate to zero out the multiplicand.

Abstract: A multiply accumulator performs a multiplication-and-addition operation for a first multiplier with N bits, a second multiplier with N bits, and an addend with M bits, wherein M is larger than 2N. The multiply accumulator includes a modified Booth encoder and a multiplication-and-addition unit. The modified Booth encoder performs a Booth encoding to either the first multiplier or its bit inversion by supplementing a multiplier sign bit behind a least significant bit of either the first multiplier or its bit inversion. The multiplication-and-addition unit includes a carry save adder tree and a sign extension adder and achieves a high speed of the multiplication-and-addition operation by simultaneously performing the multiplication and addition.

Abstract: A new partial product bit generator is used to generate a partial product bit PPji. In some embodiments, the partial product bit generator generates the partial product bit PPji from intermediate signals that are able to be generated concurrently, for example in two levels of combinatorial logic. The partial product bit PPji is then able to be generated from the intermediate signal, for example in only one level of combinatorial logic. In such embodiments, a long series of combinatorial logic operations is not required.