Abstract: Digital filters and filtering methods may employ truncation, internal rounding, and/or approximation in a summation circuit that combines multiple sets of bit products arranged by bit weight. One illustrative digital filter includes: a summation circuit coupled to multiple partial product circuits. Each partial product circuit is configured to combine bits of a filter coefficient with bits of a corresponding signal sample to produce a set of partial products. The summation circuit produces a filter output using a carry-save adder (“CSA”) tree that combines the partial products from the multiple partial product circuits into bits for two addends. The CSA tree has multiple lanes of adders, each lane being associated with a corresponding bit weight. The adders in one or more of the lanes associated with least significant bits of the filter output are approximate adders that trade accuracy for simpler implementation.

Abstract: An integrated circuit includes a bit slicing circuit with a processing circuit. The processing circuit receives discrete frequency power estimates based on an S-FSK waveform received by an S-FSK receiver associated with the bit slicing circuit. The discrete frequency power estimates are representative of digital logic levels in a series of data frames modulated using S-FSK to form the S-FSK waveform. Each data frame including at least one word. Each word includes bit periods. The processing circuit receives SNR parameters that represent a dynamic SNR for the respective discrete frequency power estimates in relation to the series of data frames. The processing circuit selects a bit slicing technique from a set of available bit slicing techniques to generate data bit values for bit periods of the discrete frequency power estimates based on the SNR parameters. A method for performing bit slicing in an S-FSK receiver is also disclosed.

Abstract: A configurable integrated circuit to compute vector dot products between a first N-bit vector and a second N-bit vector in a plurality of precision modes. An embodiment includes M slices, each of which calculates the vector dot products between a corresponding segment of the first and the second N-bit vectors. Each of the slices outputs intermediary multiplier results for the lower precision modes, but not for highest precision mode. A plurality of adder trees to sum up the plurality of intermediate multiplier results, with each adder tree producing a respective adder out result. An accumulator to merge the adder out result from a first adder tree with the adder out result from a second adder tree to produce the vector dot product of the first and the second N-bit vector in the highest precision mode.

Abstract: Integrated circuits with specialized processing blocks are provided. The specialized processing blocks may include floating-point multiplier circuits that can be configured to support variable precision. A multiplier circuit may include a first carry-propagate adder (CPA), a second carry-propagate adder (CPA), and an associated rounding circuit. The first CPA may be wide enough to handle the required precision of the mantissa. In a bridged mode, the first CPA may borrow an additional bit from the second CPA while the rounding circuit will monitor the appropriate bits to select the proper multiplier output. A parallel prefix tree operable in a non-bridged mode or the bridged mode may be used to compute multiple multiplier outputs. The multiplier circuit may also include exponent and exception handling circuitry using various masks corresponding to the desired precision width.

Abstract: A data processing device has an instruction decoder, a control logic unit, and ALU. The instruction decoder decodes instruction codes of an arithmetic instruction. The control logic unit detects the effective data width of operation data to be processed according to the decode result from the instruction decoder and determines the number of cycles for the instruction execution corresponding to the effective, data width. The ALU executes the instruction with the number of cycles of the instruction execution determined by the control logic unit.

Abstract: Circuitry for performing arithmetic operations on a plurality of inputs efficiently performs both fixed-point operations and floating-point operations. Each of at least first and second respective operator circuits operates on a respective subplurality of the plurality of inputs. Other circuitry selectively interconnects the respective operator circuits so that they can operate together or separately, according to user selection, on selected ones of (a) the full plurality of inputs, (b) individual ones of the respective subpluralities of the plurality of inputs, or (c) combinations of portions of the respective subpluralities of the plurality of inputs. At least one of the respective operator circuits includes circuits for simultaneously computing multiple different results and for selecting among the multiple different results based on an output of another one of the respective operator circuits.

Abstract: An independently timed multiplier unit includes a multiplier and a clock generator. The multiplier has a first set of semiconductor circuits in a critical path. The clock generator has a second set of semiconductor circuits configured to control a clock period of said clock generator selected to set a clock period longer than the propagation delay through the critical path of the multiplier. The clock generator may include a delay circuit having a delay to set the clock period longer than the propagation delay through the critical path of said multiplier. The clock generator uses circuit with identical logical design including the same standard cells, the same logic design or the same floor plan. Close matching of these circuit causes the multiplier and the clock generator to experience the same PVT speed variations.

Abstract: A system for fast determination of a horizontal minimum of multiple digital values including a difference circuit and a compare circuit. The difference circuit may include first and second adders in which the first adder compares upper bits of a first digital value with upper bits of a second digital value and provides a first carry output and a propagate output. The second adder compares lower bits of the first digital value with lower bits of the second digital value and provides a second carry output. The compare circuit determines whether the first digital value is greater than the second digital value based on the carry and propagate outputs. Multiple difference circuits may be used to compare each of multiple digital values with every other digital value to provide corresponding compare bits, which are then used to determine a minimum one of the digital values and its corresponding location.

Abstract: In a programmable logic device having a specialized functional block incorporating multipliers and adders, multiplication operations that do not fit neatly into the available multipliers are performed partially in the multipliers of the specialized functional block and partially in multipliers configured in programmable logic of the programmable logic device. Unused resources of the specialized functional block, including adders, may be used to add together the partial products produced inside and outside the specialized functional block. Some adders configured in programmable logic of the programmable logic device also may be used for that purpose.

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: An arithmetic unit comprising: an encoding circuit arranged to receive first and second operands each having a bit length of m bits and to generate therefrom a number n of partial products of bit length of 2m bits or less; an addition circuit having 2m columns each having n inputs, wherein bits of said partial products are applied to said inputs for combining said partial products into a result leaving certain of said inputs unused; and a rounding bit generator connected to supply a rounding bit to at least one of said unused inputs in one of said in columns at a bit position to cause said result to be rounded.

Abstract: In general, in one aspect, the disclosure describes a multiplier that includes a set of multiple multipliers configured in parallel where the set of multiple multipliers have access to a first operand and a second operand to multiply, the first operand having multiple segments and the second operand having multiple segments. The multiplier also includes logic to repeatedly supply a single segment of the second operand to each multiplier of the set of multiple multipliers and to supply multiple respective segments of the first operand to the respective ones of the set of multiple multipliers until each segment of the second operand has been supplied with each segment of the first operand. The logic shifts the output of different ones of the set of multiple multipliers based, at least in part, on the position of the respective segments within the first operand. The multiplier also includes an accumulator coupled to the logic.

Abstract: A floating point multiplier circuit includes partial product generation logic configured to generate a plurality of partial products from multiplicand and multiplier values. The plurality of partial products corresponds to a first and second portion of the multiplier value during respective first and second partial product execution phases. The multiplier also includes a plurality of carry save adders configured to accumulate the plurality of partial products generated during the first and second partial product execution phases into a redundant product during respective first and second carry save adder execution phases. The multiplier further includes a first carry propagate adder coupled to the plurality of carry save adders and configured to reduce a first and second portion of the redundant product to a multiplicative product during respective first and second carry propagate adder phases. The first carry propagate adder phase begins after the second carry save adder execution phase completes.

Abstract: An arithmetic logic unit (ALU) for use within a flight control system is provided. The ALU comprises a first register configured to receive a first operand, a second register configured to receive a second operand, and an adder coupled to the first register and the second register. The adder is configured to generate a sum of the first operand and the second operand and to generate intermediate sums that are used to determine a product of the first operand and the second operand.

Abstract: A system for performing parallel multiplication on a plurality of factors. In a binary processor, a first and a second memory have pluralities of bit-positions. The first memory holds a first value as a multiplier that will commonly serve as multiple of the factors, and the second memory holds a second value that is representative of multiple multiplicands that are other of the factors. A multiplier bit-count is determined of the significant bits in the multiplier. And a +* operation is performed with the first value and said second value a quantity of times equaling the multiplier bit-count.

Abstract: A sequential multiplier for multiplying a binary multiplier and a binary multiplicand to produce a final product. A first logic circuit generates a control signal based on the multiplier. A second logic circuit generates a partial product based on the control signal and the multiplicand. A full adder generates a partial sum and a partial carry in each of a sequence of cycles. In the first cycle the partial sum and the partial carry are both initialized to zero. In each said cycle the partial sum, the partial carry, and the partial product are added to generate a new partial sum and a new partial carry. After a last cycle, the partial sum is the final product.

Abstract: Digital mixers which permit mixing of asynchronous signals are constructed of Rapid Single Flux Quantum (RSFQ) logic elements. The logic elements may include an RSFQ non-destructive readout cell (NDRO), an RSFQ D flip-flop, an RSFQ XOR circuit, and an RSFQ T flip-flop. A binary tree arrangement of T flip-flops can be used to provide in-phase and quadrature phase-divided replicas of a reference signal. The mixing elements can be either an XOR circuit, a dual port NDRO circuit functioning as a multiplexer or an RS type NDRO functioning as an AND gate. The RSFQ logic elements utilize Josephson junctions which operate in superconducting temperature domains.

Abstract: An array multiplier comprises a partial product array including a plurality of array elements and a final carry propagate adder. Operands smaller than a corresponding dimension of the partial product array are shifted toward the most significant row or column of the array to reduce the number of array elements used to compute the product of the operands. Switching activity in the unused array elements may be reduced by turning off power to the array elements or by padding the shifted operands with zeros in the least significant bits. Additional power saving may be achieved by having bypass lines in the partial product array that bypasses non-essential array elements and by feeding partial sum and carry directly to the final carry propagate adder. Elements of the carry propagate adder may also be bypassed to achieve further power reduction.

Abstract: A method of image format conversion and remote control device using the same. Addition terms for a first layer are derived from an image conversion table. Every two addition terms are assigned to an addition group, obtaining a plurality of addition groups. The two addition terms of each addition group are added by using an adder to obtain addition terms for next layer thereafter. The bit number of the adder is equivalent to that of one addition term comprising the maximum bit number in every addition group. Finally, the addition process is repeated to obtain the operation result.

Abstract: A multiplier (42) forms a product from two signed operands without performing a sign extension of the multiplicand (A). A modified Booth's recoding of the multiplier operand (B) is begun immediately without being delayed by a sign extension operation. While recoding and partial product generation is occurring, a determination is made in parallel whether or not a sign extension adjustment term must be created. When needed, a value equal to (?B) (2N), where N is equal to a bit width of the multiplicand (A), is formed in parallel with the recoding and partial product generation. The sign extension adjustment term is coupled to a plurality of carry save adders (49, 51, 53) that compress a plurality of partial products to a sum term and a carry term. A final add stage combines the sum term and carry term to provide a product with correct sign extension.

Abstract: An apparatus comprising one or more look-up-tables (LUTs). The LUTs may be configured to provide logical functions. The one or more LUTs are generally implemented within a multiport memory.

Abstract: The invention pertains to an improved method for generating ALU instruction sequences for performing integer multiplication. The invention analytically helps to find an optimal sequence of shift, add and subtract instructions for performing integer multiplication by trying to add or subtract all powers of 2 less than the integer multiplier itself and then trying to factor evenly the resulting sum or difference by that power of 2 plus or minus one. If each such resulting factor value factors by a power of 2, the corresponding factor set is a favorable one for generating an optimal ALU instruction sequence.

Abstract: In a circuit which adds a partial product {&Sgr;(Aj*B)*2{circumflex over ( )}j (j=0, . . . , m−1)} to a provisional remainder u by using a value of inferior m bits (m is an integer not less than 2) of a number to be multiplied A and a multiplier factor &agr;, there is provided a multiplication remainder calculator which shifts inferior m bits of a provisional remainder u by continuously connecting m stages of processing circuits which perform addition of a modulus N and one-bit shift, and calculates a Montgomery product of the number to be multiplied A and the multiplier factor B by repeating this processing, wherein a multiple number of the multiplier factor can be calculated by inhibiting one-bit shift of the processing circuits.

Abstract: A multiplier for computing a final product of a first operand and a second operand comprising a multiplier array for forming a product of the first operand and second operand in carry-save form; a carry-save adder for adding said carry-save partial products and an accumulatd sum to produce a carry and save values; a carry-lookahead adder for adding said carry and save values to produce a product value and a carry-out value; a general purpose adder for adding said carry-out and said product value to produce said final product.

Abstract: Disclosed is a method and apparatus for accomplishing high speed multiplication of binary numbers using a single clock cycle to achieve the same computational power provided by the multiple clock cycle shift register configurations or the asynchronous multistate logic configurations of the prior art. “Virtual shifts” are achieved by allocating one or more positions, within a register storing the partial products, as place holders, typically zeroes. These place holders can be inserted in a single clock cycle and do not require the multi-staged shift register configurations of the prior art.

Abstract: Implementation of multipliers in an FPGA or similar device containing an array or other aggregation of small processor devices is a significant difficulty, leading to increased cost as a result of the silicon area consumed thereby.

Abstract: An efficient demodulation and low pass filter structure comprises a shift-add-negate structure that effectively multiplies each received sample by a combined demodulation and filter coefficient, and an accumulator that accumulates the products. Low pass filter coefficients are selected such that the shift-add-negate structure implements multiplications by shifts, adds, and negations. In the preferred embodiment, the demodulation and low pass filter structure outputs three complex samples per symbol.

Abstract: This application describes a method of multiplying numbers represented in multiple-word chains. The multiplication scheme allows for the multiplication of both signed and unsigned numbers of varying lengths. The multiplier block 30 executes a 17-bit by 17-bit two's complement multiply and multiply-accumulate in a single instruction cycle. A 4-bit shift value register with a 4 to 16 bit decoder 35 allows the multiplier to do a 1-16 bit barrel shift on either a 16-bit operand or an (N×16)-bit chain operand.

Abstract: A multiplier including a processor that generates at least one N by M array of partial products. The processor includes a first section that performs a first operation that generates an N by M array of partial products representing low order bits, and a second section that performs a second operation that generates an N by M array of partial products representing high order bits. The multiplier also includes a compressor that compresses the N by M array of partial products representing low order bits after the first operation and generates a plurality of carry bits that are utilized in the second operation.

Abstract: The present invention relates to a high speed sample and hold circuit which comprises a plurality of sample and hold subcircuits coupled in parallel between an input and an output. The circuit also comprises a calibration circuit coupled to the plurality of sample and hold subcircuits. The calibration circuit is operable to modify a hold signal for one or more of the plurality of sample and hold subcircuits to thereby reduce timing mismatch between the plurality of sample and hold subcircuits and distortion associated therewith. The present invention also comprises a method of reducing timing mismatch in a high speed, parallel coupled sample and hold circuit. The method comprises detecting timing mismatch associated with a plurality of sample and hold subcircuits and modifying a hold signal for one or more of the subcircuits.

Abstract: A method and apparatus including conditional add and conditional add/subtract instructions are provided for use in the instruction set of a medical device instruction processor. More specifically, the conditional add and add/subtract instructions are provided to add two operands if a predetermined condition is satisfied within the instruction processor hardware. Additionally, the conditional add/subtract instruction may be used to subtract one operand from another operand if the predetermined condition is not satisfied. These instructions are adapted for use in implementing an efficient, interruptible, firmware-controlled multiplication or division mechanism. The inventive system allows multiplication or division operations to be interrupted at various intermediate points during the multiplication or division operation to thereby reducing interrupt latency.

Abstract: A parallel multiplier includes m multiplexers and a plurality of adders. The multiplexers receive an n-bit multiplicand and n-bit zero (0) through two input terminals, respectively, and one (1) bit of a m-bit multiplier through a select terminal to selectively output the n-bit multiplicand when the one bit of the m-bit multiplier is “1 ” and the n-bit zero (0) when the one bit of the m-bit multiplier is “0”. The adders receive two of the n-bit output data from the multiplexers to output an n+2 bit partial product or an n+m bit product by adding two neighboring output data from the multiplexers after 1 bit downshifting the (less significant) neighboring output data corresponding to the less significant bit of the m-bit multiplier. A final adder can output an n+m bit product by adding two (n+x bit) partial products after downshifting a selected one.

Abstract: An adder tree includes several partial product generators, each generating a bit of equal weight. An adder receives the bits and provides a carry bit to a logic unit. The logic unit propagates the carry bit to the next more significant column in response to a carry enable instruction. The logic unit outputs a bit that is independent of the carry bit in response to a lack of a carry enable instruction.

Abstract: The present invention provides a method and an apparatus for performing multiply operation of floating point data in 2-cycle pipeline scheme, which can be applied to pipelined data path so that it is always capable of processing floating point data as long as the data is not contiguous, for reducing the area of the multiplier by reducing the number of basic cells used to 1/3 of that of basic cells used in conventional techniques.

Abstract: A multiplier capable of performing both signed and unsigned scalar and vector multiplication is disclosed. The multiplier is configured for use in a microprocessor and may include a partial product generator, a selection logic unit, and an adder. The multiplier is configured to receive signed or unsigned multiplier and multiplicand operands in scalar or packed vector form. The multiplier is also configured to receive a first control signal indicative of whether signed or unsigned multiplication is to be performed and a second control signal indicative of whether vector multiplication is to be performed. The multiplier is configured to calculate an effective sign for the multiplier and multiplicand operands based upon each operand's most significant bit and the control signal. The effective signs may then be used by the partial product generation unit and the selection logic to create and select a number of partial products according to Booth's algorithm.

Abstract: A new logic with shift switches incorporating novel parallel compressors and counters called C4 and (7,3) families. This shift switch logic deals with modulo arithmetic operations. It employs a type of special digital signals, called state signals (as a major addition to the binary signals), and a set of electronic components, called shift switches, to manipulate such signals and conduct the logic operations. A useful modulo arithmetic produces two values: a remainder and a quotient, given two small (non-negative) integers. One integer is a variable numerator represented by a set of input digital signals (including regular and/or state signals), while the other is a dominator (base or radix) provided by the shift switch circuit as a parameter. Using C4 and (7,3) devices, two novel, parallel-structured, full array, 64.times.64 floating point multiplier schemes are disclosed.

Abstract: A number of adder structures (also referred to herein as "tiles" and "Quickadders.TM.") are provided which may be constructed with positively and/or negatively weighted and signed inputs and outputs and which may be placed so as to span one or more bitslices of a multiplier array. In a second aspect of the present invention, groups of replicable circuitry columns are provided for forming multiplier arrays for multiplying binary numbers X and Y to obtain a binary product Z. These groups of columns of circuitry include left column groups to handle X-inputs to the array, internal column groups, and right column groups to handle outputs to a CLA adder/subtractor (or equivalent) for processing the MSBs of the product. The LSBs of the product are produced directly by the array. The groups may be thought of as replacing 2, 3 or 4 conventional columns of full-adder circuitry of a basic array such as that shown in FIGS. 1 and 2.

Abstract: A two-bit Booth multiplier circuit performs two-bit multiplication iterations using a single adder while retaining the same data path width and the multiplicand multiples of a single-bit Booth multiplier circuit. The two-bit Booth multiplier circuit halves the number of multiplier iterations of a single-bit multiplier. A multiplier circuit includes an adder having a first input terminal, a second input terminal, and an output terminal and a plurality of shift registers. The registers include a multiplicand register having an output terminal connected to the first input terminal of the adder, a temporary shift register having an output terminal connected to the second input terminal of the adder and having an input terminal connected to the output terminal of the adder, and a multiplier shift register having an input terminal connected to the output terminal of the adder and the multiplier shift register and having an output terminal.