A multiplier has a pair of charge reservoirs. The pair of charge reservoirs are connected in series. A first charge movement device induces charge movement to or from the pair of charge reservoirs at a same rate. A second charge movement device induces charge movement to or from one of the pair of reservoirs, the rate of charge movement programmed to one of add or remove charges at a rate proportional to the first charge movement device. The first charge movement device loads a first charge into a first of the pair of charge reservoirs during a first cycle. The first charge movement device and the second charge movement device remove charges at a proportional rate from the pair of charge reservoirs during a second cycle until the first of the pair of charge reservoirs is depleted of the first charge. The second charge reservoir thereafter holding the multiplied result.

A MAC operating device comprising a plurality of operation circuits respectively including an operation capacitor and a plurality of switches; and a division capacitor, wherein one end of the operation capacitor is respectively connected to a first operation switch connected to an input terminal and a first reset switch connected to a ground terminal, and the other end of the operation capacitor is connected to both a second operation switch connected to a division capacitor and a second reset switch connected to the ground terminal is provided.

A MAC operating device comprising a plurality of operation circuits respectively including an operation capacitor and a plurality of switches; and a division capacitor, wherein one end of the operation capacitor is respectively connected to a first operation switch connected to an input terminal and a first reset switch connected to a ground terminal, and the other end of the operation capacitor is connected to both a second operation switch connected to a division capacitor and a second reset switch connected to the ground terminal is provided.

An energy-efficient multiplication circuit uses analog multipliers and adders to reduce the distance that data has to move and the number of times that the data has to be moved when performing matrix multiplications in the analog domain. The multiplication circuit is tailored to bitwise multiply the innermost product of a rearranged matrix formula generate a matrix multiplication result in form of a current that is then digitized for further processing.

An energy-efficient multiplication circuit uses analog multipliers and adders to reduce the distance that data has to move and the number of times that the data has to be moved when performing matrix multiplications in the analog domain. The multiplication circuit is tailored to bitwise multiply the innermost product of a rearranged matrix formula generate a matrix multiplication result in form of a current that is then digitized for further processing.

A method for validating a capacitance measurement device including, sending a first drive signal from a capacitance measurement device to a capacitor emulator, modifying the first drive signal by an four quadrant analog multiplier, directing the modified signal across a capacitor to produce a return signal, sending the return signal to the capacitance measurement device to validate the capacitor, and validating the return signal against an expected return signal by the capacitance measurement device.

A product-sum operation device includes a product operator and a sum operator. The product operator includes a plurality of variable-input product operation elements and a plurality of fixed-input product operation elements. Each of the plurality of variable-input product operation elements and the plurality of fixed-input product operation elements and is a resistance change element. The product-sum operation device includes variable input units and that input a variable signal to a plurality of variable-input product operation elements and fixed input units and that input a determined signal to the plurality of fixed-input product operation elements and in synchronization with the variable signal. The sum operator includes an output detector that determines the sum of outputs from the plurality of variable-input product operation elements and outputs from the plurality of fixed-input product operation elements.

A product-sum operation device includes a product operator and a sum operator. The product operator includes a plurality of variable-input product operation elements and a plurality of fixed-input product operation elements. Each of the plurality of variable-input product operation elements and the plurality of fixed-input product operation elements and is a resistance change element. The product-sum operation device includes variable input units and that input a variable signal to a plurality of variable-input product operation elements and fixed input units and that input a determined signal to the plurality of fixed-input product operation elements and in synchronization with the variable signal. The sum operator includes an output detector that determines the sum of outputs from the plurality of variable-input product operation elements and outputs from the plurality of fixed-input product operation elements.

Electric charges depending on values of N.sup.+ electric signals and values of corresponding positive loads are held in first capture-and-storage circuitry. Electric charges having a size depending on values of (N−N.sup.+) electric signals and corresponding absolute values of negative loads are held in second capture-and-storage circuitry. A sum of N.sup.+ multiplied values obtained by multiplying each of the positive loads by each of the values of the N.sup.+ electric signals is calculated when a voltage held in the first capture-and-storage circuitry reaches a first threshold. A sum of (N−N.sup.+) multiplied values obtained by multiplying each of the absolute values by each of the values of the (N−N.sup.+) electric signals is calculated when a voltage held in the second capture-and-storage circuitry reaches a second threshold A sum of N multiplied values is obtained by subtracting the sum of (N−N.sup.+) multiplied values from the sum of N.sup.+ multiplied values.

An analog vector-matrix multiplication circuit is achieved by using a programmable storage device array. In a programmable semiconductor device array, gates of all of programmable semiconductor devices of each row are all connected to the same analog voltage input end. M rows of programmable semiconductor devices are correspondingly connected to M analog voltage input ends. Drains (or sources) of all of programmable semiconductor devices of each column are all connected to the same bias voltage input end. N columns of programmable semiconductor devices are correspondingly connected to N bias voltage input ends. Sources (or drains) of all of programmable semiconductor devices of each column are all connected to the same analog current output end. The N columns of programmable semiconductor devices are correspondingly connected to N analog current output ends. Threshold voltages of the programmable semiconductor devices are controlled, such that each programmable semiconductor device can be regarded as a variable equivalent analog weight, thereby achieving the matrix multiplication function.