Abstract: A new class of multiplier cells (analog or digital) is derived from a 1-bit full adder and an AND gate. The 1-bit full adder is derived from first and second majority gates. The multiplier cell can also be implemented with a combination of two majority gates with majority and AND functions integrated in each of them. The two majority gates are coupled. Each of the first and second majority logic gates comprise a capacitor with non-linear polar material. The first and second majority gates receive the two inputs A and B that are to be multiplied. Other inputs received by the first and second majority gates are carry-in input, a sum-in input, and a bias voltage. The bias voltage is a negative voltage, which produces an integrated AND function in conjunction with a majority function. The second majority gate receives additional inputs, which are inverted output of the first majority gate.

Abstract: A low power sequential circuit (e.g., latch) uses a non-linear polar capacitor to retain charge with fewer transistors than traditional CMOS sequential circuits. In one example, a sequential circuit includes pass-gates and inverters, but without a feedback mechanism or memory element. In another example, a sequential uses load capacitors (e.g., capacitors coupled to a storage node and a reference supply). The load capacitors are implemented using ferroelectric material, paraelectric material, or linear dielectric. In one example, a sequential uses minority, majority, or threshold gates with ferroelectric or paraelectric capacitors. In one example, a sequential circuit uses minority, majority, or threshold gates configured as NAND gates.

Abstract: An in-memory vector addition method for a dynamic random access memory (DRAM) is disclosed which includes consecutively transposing two numbers across a plurality of rows of the DRAM, each number transposed across a fixed number of rows associated with a corresponding number of bits, assigning a scratch-pad including two consecutive bits for each bit of each number being added, two consecutive bits for carry-in (Cin), and two consecutive bits for carry-out-bar (Cout), assigning a plurality of bits in a transposed orientation to hold results as a sum of the two numbers, for each bit position of the two numbers: computing the associated sum of the bit position; and placing the computed sum in the associated bit of the sum.

Abstract: A low power sequential circuit (e.g., latch) uses a non-linear polar capacitor to retain charge with fewer transistors than traditional CMOS sequential circuits. In one example, a sequential circuit includes pass-gates and inverters, but without a feedback mechanism or memory element. In another example, a sequential uses load capacitors (e.g., capacitors coupled to a storage node and a reference supply). The load capacitors are implemented using ferroelectric material, paraelectric material, or linear dielectric. In one example, a sequential uses minority, majority, or threshold gates with ferroelectric or paraelectric capacitors. In one example, a sequential circuit uses minority, majority, or threshold gates configured as NAND gates.

Abstract: A memory device is provided. The memory device includes: a cell region including a first metal pad, a memory cell in the cell region configured to store weight data, a peripheral region including a second metal pad and vertically connected to the memory cell by the first metal pad and the second metal pad, a buffer memory in the peripheral region configured to read the weight data from the memory cell, an input/output pad in the peripheral region configured to receive input data; and a multiply-accumulate (MAC) operator in the peripheral region configured to receive the weight data from the buffer memory and receive the input data from the input/output pad to perform a convolution operation of the weight data and the input data, wherein the input data is provided to the MAC operator during a first period, and wherein the MAC operator performs the convolution operation of the weight data and the input data during a second period overlapping with the first period.

Abstract: A multiplication accumulating device and a method thereof are provided. The multiplication accumulating device includes a product generator, a plurality of registers, a product reducer, and an adder. The product generator performs a product operation on a multiplicand and a multiplier to generate a product result of 2N?1 columns. The product reducer is used to append data from a portion of the plurality of registers to the columns in the product result to generate an appending result of 2N?1 columns. The product reducer performs a reduction operation on the appending result according to a column height of each column in the appending result to obtain a reduced result. The product reducer renews the data in the plurality of registers according to the reduced result. The adder adds the data in the plurality of registers according to an accumulation signal to generate a multiplication accumulating operation result.

Abstract: The present disclosure relates to an apparatus that includes decoding circuitry that decodes a single instruction. The single instruction includes an identifier of a first source operand, an identifier of a second source operand, an identifier of a destination, and an opcode indicative of execution circuitry is to multiply from the identified first source operand and the identified second source operand and store a result in the identified destination. Additionally, the apparatus includes execution circuitry to execute the single decoded instruction to calculate a dot product by calculating a plurality of products using data elements of the identified first and second operands using values less precise than the identified first and second source operands, summing the calculated products, and storing the summed products in the destination.

Abstract: In a processing in memory (PIM) method using a memory device, m*n multiplicand arrangement bits are stored in m*n memory cells by copying and arranging m multiplicand bits of a multiplicand value and m*n multiplier arrangement bits are stored in m*n read-write unit circuits corresponding to the m*n memory cells by copying and arranging n multiplier bits of a multiplier value. The m*n multiplicand arrangement bits stored in the m*n memory cells are selectively read based on the m*n multiplier arrangement bits stored in the m*n read-write unit circuits, and m*n multiplication bits are stored in the m*n read-write unit circuits based on the selectively read m*n multiplicand arrangement bits. A multiplication value of the multiplicand value and the multiplier value is determined based on the m*n multiplication bits stored in the m*n read-write unit circuits.

Abstract: A sensor includes an accelerometer, which, in operation, generates accelerometer data, and digital signal processing circuitry. The digital signal processing circuitry, in operation, generates, based on the generated accelerometer data, a value indicative of a cosine of an angle between an acceleration vector associated with current accelerometer data and a reference acceleration vector, compares the generated value indicative of the cosine of the angle between the vector associated with current accelerometer data and the reference acceleration vector with one or more thresholds and generates a tilt signal based on the comparison of the generated value indicative of the cosine of the angle between the vector associated with current accelerometer data and the reference acceleration vector with the one or more thresholds. The tilt signal may be used as an interrupt signal to an application processor.

Abstract: Embodiments of the present disclosure pertain to multimodal digital multiplier circuits and methods. In one embodiment, partial product outputs of digital multiplication circuits are selectively inverted based on a mode control signal. The mode control signal may be set based on a format of the operands input to the multiplier. Example embodiments of the disclosure may multiply combinations of signed and unsigned input operands using different modes.

Abstract: The present disclosure discloses an adder device, a data accumulation method and a data processing device. The adder device comprises: a first adder module provided with an adder tree unit, composed of a multi-stage adder array, and a first control unit, wherein the adder tree unit accumulates data by means of step-by-step accumulation based on a control signal of the first control unit; a second adder module comprising a two-input addition/subtraction operation unit and a second control unit, and used for performing an addition or subtraction operation on input data; a shift operation module for performing a left shift operation on output data of the first adder module; an AND operation module for performing an AND operation on output data of the shift operation module and output data of the second adder module; and a controller module.

Abstract: Circuitry that accepts a data input and an enable input, and generates an output sum based on the data input includes an input stage circuit that includes an input register. The input register accepts the enable input. The circuitry further includes a systolic register operatively connected to the input stage circuit, and the systolic register is operated without any enable connection. The circuitry further includes a multiplier connected to the systolic register, which is configured to generate a product value. The circuitry further includes an output stage circuit that includes an adder that calculates the output sum based least in part on the product value.

Abstract: A field programmable threshold-logic array (FPTLA) includes a number of threshold logic gates and a number of programmable interconnect elements. Each one of the programmable interconnect elements are connected between two or more of the threshold logic gates, such that the programmable interconnect elements route signals between the threshold logic gates. By using threshold logic gates for the FPTLA, the size of the FPTLA may be significantly smaller than conventional solutions. Further, using threshold logic gates results in significant improvements in the computation speed of the FPTLA when compared to conventional solutions.

Abstract: A multiplier of a binary number A by a binary number B may be configured to add each term AiBj with a left shift by i+j bits, where Ai is the bit of weight i of number A, and Bj the bit of weight j of number B. The multiplier may include a first counter associated with the number A and may count modulo n and be paced by a clock. The multiplier may include a second counter associated with the number B and paced by the clock. Switching circuitry may produce the terms AiBj by taking the content of the first and second counters respectively as weights i and j. Shifting circuitry is configured to shift the content of one of the first and second counters when the other counter has achieved a revolution.

Abstract: Method and apparatus for multiplying a signed first operand na bits and a signed second operand nb bits, wherein na and nb are different positive integer numbers, the method comprising generating single bit products of pairs of a single bit from the signed first operand and a single bit from the signed second operand with a logical AND function to produce na times nb single bit products, selectively inverting for the signed first operand and the signed second operands the single bit products of the first operand bit na-1 multiplied with the second operand bits 0 to nb-2, selectively inverting the single bit products of the signed second operand bits 0 to na-2 multiplied with the signed second operand bit nb-1, after the step of inverting adding the single bit products in accordance with their respective order for producing an intermediate product, and adding a ‘1’ bit value at bit positions nb-1, na-1 and na+nb-1 for receiving a final product.

Abstract: A Generalized Programmable Counter Array (GPCA) is a reconfigurable multi-operand adder, which can be reprogrammed to sum a plurality of operands of arbitrary size. The GPCA is configured to compress the input words down to two operands using parallel counters. Resulting operands are then summed using a standard Ripple Carry Adder to produce the final result. The GPCA consists of a linear arrangement of identical compressor slices (CSlice).

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: Methods, apparatus and systems for large number multiplication. A multiplication circuit is provided to compute the product of two operands (A and B), at least one of which is wider than a width associated with the multiplication circuit. Each of the operands includes contiguous ordered word-wide operand segments (Aj and Bi) characterized by specific weights j (integer from 0 to k) and i (integer from 0 to m). The multiplication circuit executes a matrix of word-wide operand segment pair multiplication operations. Multiplication operations are performed on a pair of rows at one time. For each pair of rows, a pair of corresponding Bi word-wide operand segments are read from a memory and word-wide operand segment pair multiplication operations (Aj*Bi) are iteratively performed for each of k+2 columns. For each column a maximum of two additional memory read operations and one memory write operation is required.

Abstract: A method for implementing sign extension within a multi-precision multiplier is described. The method includes receiving a first input within a multiplier core of the multiplier, receiving a second input within the multiplier core, and creating partial products in the multiplier core using the first and second inputs. The method also includes summing up the partial products in a partial product reduction tree in the multiplier core. The method also includes performing sign extension within the partial product reduction tree of the multiplier core by adding a value to a partial product of the partial product reduction tree. The method further includes computing an output from the partial product reduction tree, the output including a final product of the first and second inputs signed extended to a desired width.

Abstract: Method, apparatus, and program means for performing a dot-product operation. In one embodiment, an apparatus includes execution resources to execute a first instruction. In response to the first instruction, said execution resources store to a storage location a result value equal to a dot-product of at least two operands.

Abstract: A multiplication logic circuit comprises array generation logic and array reduction logic. The array reduction logic comprises array reduction logic for a first level of array reduction which comprises maximal length parallel counters for reducing maximal length columns. The output of the maximal length parallel counters are then further reduced by a second level of reduction logic comprising logic circuits with asymmetric delays in order to compensate for the differential delays experienced by the outputs of the maximal length parallel counters.

Abstract: A parallel counter comprises logic for generating output bits as symmetrical functions of the input bits. The parallel counter can be used in a multiplication circuit. A multiplication circuit is also provided in which an array of combinatins of each bit of a binary number with each other bit of another binary number is generated having a reduced from in order to reduce the steps required in array reduction.

Abstract: A parallel counter comprises logic for generating output bits as symmetrical functions of the input bits. The parallel counter can be used in a multiplication circuit. A multiplication circuit is also provided in which an array of combinations of each bit of a binary number with each other bit of another binary number is generated having a reduced form in order to reduce the steps required in array reduction.

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: A linear transform apparatus for implementing a linear transform on input data values to produce linear transformed output data, the apparatus comprising: input means for inputting input data values one after another to each of a series of multiplication means; a series of multiplication means interconnected with the input means for multiplying a current input data value by a constant to produce a current multiplier output; an interconnection network interconnecting the series of multiplication means to predetermined ones of a series of signed accumulator means; a series of signed accumulator means each interconnected to the interconnection network, each of the signed accumulator means producing an intermediate accumulator output by accumulating a corresponding one of the current multiplier outputs with a corresponding previous intermediate accumulator output, each of the signed accumulator means outputting the intermediate accumulator output as a corresponding linear transformed output data value.

Abstract: A method and an apparatus for implementing mixed scalar and vector values in a digital processing system. In one embodiment, a digital processing system, which contains processing unit and memories, is capable of identifying a first data in a first scalar register and a second data in a vector register. Upon fetching the first data as a first operand and the second data as a second operand, the processing unit performs an operation between the first and second operands in response to an operator. After operations, the result is subsequently stored in a second scalar register.

Abstract: Parallel multipliers and techniques for reducing Wallace-trees in parallel multipliers to achieve fewer reduction stages. The parallel multipliers of the present invention, in one embodiment, require one fewer stage of reduction than conventional multipliers proposed by Wallace and Dadda. Accordingly, fewer adder components are required. The speed of the parallel multipliers of the present invention is also improved due to the fewer number of reduction stages. In another embodiment, the method of the present invention is applicable to signed multiplication and includes a step of performing trial reduction on an input matrix that has a maximum number of nodes per column K. The trial reduction step is performed with a reduction target of &dgr;L-2 nodes where &dgr;L-1<K≦&dgr;L. If maximum number of nodes per column in the resulting matrix does not exceed &dgr;L-2, then reduction steps are performed to generate a reduction tree having L-1 reduction stages.

Abstract: An improved parallel multiplier capable of operating an addition operation by connecting a plurality of dividers sequentially, thus providing more simple circuit and reducing operating time thereof, which includes NXM AND-gates each for ANDing each multiplier bit ranging from a least significant bit to a most significant bit with each multiplicand bit in case of multiplying “N” multiplicand bits and “M” multiplier bits and for performing a partial multiplication and for outputting a least significant bit as a result of the multiplication; and a plurality of input-bits dividers, having 2-, 3-, and 4-input-bits dividers, for receiving an output bit of a corresponding location among a rearranged output bit and a quotient bit outputted from a proceeding input bit in case that the output bits of the AND-gates is shifted to the left by a bit in accordance with a conventional binary multiplication method and for outputting a quotient bit and a remaining bit corresponding to each bit of a mult

Abstract: A method and apparatus for including in a processor instructions for performing multiply-add operations on packed data. In one embodiment, a processor is coupled to a memory. The memory has stored therein a first packed data and a second packed data. The processor performs operations on data elements in said first packed data and said second packed data to generate a third packed data in response to receiving an instruction. At least two of the data elements in this third packed data storing the result of performing multiply-add operations on data elements in the first and second packed data.

Abstract: A booth decoder decodes A or −A according to a booth algorithm, depending upon whether A×B or −A×B should be multiplied. A partial multiplier/partial adder circuit 30 generates partial products of A×B or −A×B following to a result of the decoding, and sequentially adds these partial products. Data C, or data made by inverting bits of C, is input to the partial multiplier/partial adder circuit 30, depending upon whether C should be added or −C should be added to the result of multiplication. Also the data C or data made by inverting bits of C are sequentially added by the partial multiplier/partial adder circuit 30. A final adder circuit 50 executes final addition of these partial products, and adds 1 when −C should be added. Thus, Z=±(A×B)±C (the order of signs being variable) can be calculated.

Abstract: Bit-serial processors quickly multiply multiple-bit operands using significantly fewer clock cycles as compared to conventional bit-serial implementations. Exemplary embodiments process groups of operand bits simultaneously to provide the significant speed increases. Advantageously, however, the exemplary embodiments utilize logic and memory architectures which are fully compatible with, and fully useful for, conventional bit-serial applications, and the embodiments thus provide fast multiple-bit multiplications while at the same time providing all of the advantages typically associated with conventional bit-serial processors.

Abstract: A multiplier circuit multiplies together both natural and two's complement binary numbers, which it receives in the form of electric signals having predetermined logic values, that are applied to input terminals of logic gating circuits. The logic gating circuits provide partial products of the bits of the two binary factors, and a combinatorial network provides the final sum of the partial products. The partial multiplications that include at least one of the more significant bits of the operands are performed by logic gating circuits which can be enabled to also carry out a two's complement partial multiplication. The multiplier circuit further includes additional logic gating circuits which supply the combinatorial network with additive constants with predetermined logic values unrelated to the factors.

Abstract: A multiplier generates an array of partial products. The partial products are reduced in a converter having cells defining rows and columns. Cells adjacent to adders alternate between a cell that provides non-inverted outputs and a cell that provides inverted outputs, such that alternate rows of cells operate on non-inverted data and the intervening rows of cells operate on inverted data. A multiplexer for receiving the outputs from a row of cells may be an inverting multiplexer or a non-inverting multiplexer depending on the cell arrangement.

Abstract: A computer-based method and system is disclosed that automates the design and layout of digital multiplier circuits. The preferred method utilizes an automatic design generator having a user interface which receives design requirements for a digital multiplier circuit design. A digital multiplier design generator receives the design requirements for the digital multiplier and retrieves relevant component implementations from a component library. Stored digital multiplier benchmarks are then retrieved from a benchmark memory and applied to corresponding digital multipliers to determine which of the various implementations optimally satisfies the user design requirements. Once the optimal digital multiplier implementation is selected, the digital multiplier design generator produces a logic design including a netlist and a physical design including design directives which are then used to place and route the digital multiplier as a finished layout.

Abstract: A processor having a first and second storage having a first and second packed data, respectively. Each packed data includes a first, second, third, and fourth data element. A multiply-add circuit is coupled to the first and second storage areas. The multiply-add circuit includes a first, second, third, and fourth multiplier, wherein each of the multipliers receives a corresponding set of said data elements. The multiply-add circuit further includes a first adder coupled to the first and second multipliers, and second adder coupled to the third and fourth multipliers. A third storage area is coupled to the adders. The third storage area includes a first and second field for saving output of the first and second adders, respectively, as first and second data elements of a third packed data.

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 comprises 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 method and apparatus for including in a processor instructions for performing multiply-add operations on packed data. In one embodiment, a processor is coupled to a memory. The memory has stored therein a first packed data and a second packed data. The processor performs operations on data elements in said first packed data and said second packed data to generate a third packed data in response to receiving an instruction. At least two of the data elements in this third packed data storing the result of performing multiply-add operations on data elements in the first and second packed data.

Abstract: In a processor for performing operations including an addition of a plurality of multiple bit data, values on common places of a plurality of multiple bit data are entered in parallel into number detectors set for respective places, the number of the high signals in the input values is output in the binary notation, and outputs from a plurality of NDs are added by full adders to execute a high speed operation without carries. In addition, values with no common places are integrated into single data before being added.

Abstract: A sum-of-products arithmetic unit includes a coefficient register, a data register, a multiplier, an adder, and a data bus used for the transfer of data to and from an external unit. Provision is made to allow addresses in the data register in which sum-of-products arithmetic data is to be stored to be specified without externally specifying an individual address in the data register for each piece of arithmetic data. This provision comprises an automatic data batch storage section, automatic address setting section, or address setting section.

Abstract: A multiplier circuit which multiplies together both natural and two's complement binary numbers, which it receives in the form of electric signals having predetermined logic values, that are applied to input terminals of logic gating circuits. The logic gating circuits provide partial products of the bits of the two binary numbers, and a combinatorial network provides the final sum of the partial products. The partial products that include at least one of the more significant bits of either of the operands are performed by logic gating circuits which can be enabled to complement the partial product. The multiplier circuit further includes additional logic gating circuits which supply the combinatorial network with additive constants with predetermined logic values.

Abstract: A multiplier generates an array of partial products. The partial products are reduced in the more significant side of the array assuming a carry-out from the less significant side of the array as taking on a first state to produce a first set of reduced products. The partial products are also reduced in the more significant side of the array assuming a carry-out from the less significant side of the array as taking on a second state to produce a second set of reduced products. Both sets of reduced partial products are generated in parallel with the carry-out from the least significant side. The first set of reduced products are selected as the reduced products of the more significant side of the array when the carry-out from the less significant side of the array takes on the first state. The second set of reduced products are selected as the reduced products of the more significant side of the array when the carry-out from the less significant side of the array takes on the second state.

Abstract: A multiplier circuit which multiplies together both natural and two's complement binary numbers, which it receives in the form of electric signals having predetermined logic values, that are applied to input terminals of logic gating circuits. The logic gating circuits provide partial products of the bits of the two binary numbers, and a combinatorial network provides the final sum of the partial products. The partial products that include at least one of the more significant bits of either of the operands are performed by logic gating circuits which can be enabled to complement the partial product. The multiplier circuit further includes additional logic gating circuits which supply the combinatorial network with additive constants with predetermined logic values.