A Bias Unit Element (UE) has a digital input, a sign input, and a chop clock. The sign input is exclusive ORed with the chop clock to generate a signed chop clock. Each Bias UE comprises a positive Bias UE and a negative Bias UE, each comprising groups of NAND gates generating an output and a complementary output, each of which are coupled to differential charge transfer lines through binary weighted charge transfer capacitors to a differential charge transfer bus comprising a positive charge transfer line and a negative charge transfer line. The chopped sign input enables the positive Bias UE when the sign bit is positive and enables the negative Bias UE when the sign bit is negative.

A Bias Unit Element (UE) has a digital input, a sign input, and a chop clock. The sign input is exclusive ORed with the chop clock to generate a signed chop clock. Each Bias UE comprises a positive Bias UE and a negative Bias UE, each comprising groups of NAND gates generating an output and a complementary output, each of which are coupled to differential charge transfer lines through binary weighted charge transfer capacitors to a differential charge transfer bus comprising a positive charge transfer line and a negative charge transfer line. The chopped sign input enables the positive Bias UE when the sign bit is positive and enables the negative Bias UE when the sign bit is negative.

An arithmetic apparatus used for a neural network includes a plurality of digital-time conversion circuits connected in series and a time-digital conversion circuit connected to a last digital-time conversion circuit in the series. Each of the digital-time conversion circuits is configured to delay a first input time signal by a variable amount, delay a second input time signal by a fixed amount, and output the delayed first and second input time signals respectively as either first and second output time signals or second and first output time signals, in accordance with the input data. The time-digital conversion circuit is configured to generate a digital output signal by comparing first and second output time signals from the last digital-time conversion circuit.

Provided in one example is a nonvolatile memory cross-bar array. The array includes: a number of junctions formed by a number of row lines intersecting a number of column lines; a first set of controls at a first set of the junctions coupling between a first set of the row lines and a first set of the column lines; a second set of controls at a second set of the junctions coupling between a second set of the row lines and a second set of the column lines; and a current collection line to collect currents from the controls of the first set and the second set through their respective column lines and output a result current corresponding to a sum of a first dot product and a second dot product.

A method of performing Principal Component Analysis is provided. The method includes receiving, by a computing device, evolving data for processing/visualization. The method further includes, by the computing device, a dimensionality for reducing of the evolving data using the PCA, wherein the PCA is performed on analog crossbar hardware. The method also includes using, by the computing device, the evolving data for visualization having the dimensionality thereof reduced by the principal component analysis for a further application.

A method of performing Principal Component Analysis is provided. The method includes receiving, by a computing device, evolving data for processing/visualization. The method further includes, by the computing device, a dimensionality for reducing of the evolving data using the PCA, wherein the PCA is performed on analog crossbar hardware. The method also includes using, by the computing device, the evolving data for visualization having the dimensionality thereof reduced by the principal component analysis for a further application.

An adder circuit inhibiting overflow is provided. A first memory, a second memory, a third memory, and a fourth memory are included. A step of supplying first data with a sign to the first memory and supplying the first data with a positive sign stored in the first memory, to the second memory; a step of supplying the first data with a negative sign stored in the second memory, to the third memory; a step of generating second data by adding the first data with a positive sign stored in the second memory and the first data with a negative sign stored in the third memory; and a step of storing the second data in the fourth memory are included. When the second data stored in the fourth memory are all second data with a positive sign or all second data with a negative sign, all the second data stored in the fourth memory are added.

A method of obtaining a dot product includes applying a number of first voltages to a corresponding number of row lines within a memristive cross-bar array to change the resistive values of a corresponding number of memristors located a junctions between the row lines and a number of column lines. The first voltages define a corresponding number of values within a matrix, respectively. The method further includes applying a number of second voltages to a corresponding number of the row lines within the memristive cross-bar array. The second voltages define a corresponding number of vector values. The method further includes collecting the output currents from the column lines. The collected output currents define the dot product.

A double bias dot-product engine for vector processing is described. The dot product engine includes a crossbar array having N×M memory elements to store information corresponding to values contained in an N×M matrix, each memory element being a memristive storage device. First and second vector input registers including N voltage inputs, each voltage input corresponding to a value contained in a vector having N×1 values. The vector input registers are connected to the crossbar array to supply voltage inputs to each of N row electrodes at two locations along the electrode. A vector output register is also included to receive voltage outputs from each of M column electrodes.

Memristive computation of a cross product is disclosed. One example is a crossbar array of memory elements that include a number of column lines perpendicular to a number of row lines, a memory element located at each intersection of a row line and a column line. A programming voltage is applied at each memory element to change a resistance value to represent a respective entry in a skew symmetric matrix representing a first vector, and an input voltage is applied along each row line to represent a dimensional component of a second vector. Sensors located at each column line measure output voltages along column lines, where the output voltages are generated by applying input voltages received by memory elements located along the row line to resistance values of the respective memory elements. Differential amplifiers collate the output voltages for pairs of sensors to generate dimensional components of the cross product.