A computer-implemented method for coding a digital signal intended to be processed by a digital computing system includes the steps of: receiving a sample of the digital signal quantized on a number N.sub.d of bits, decomposing the sample into a plurality of binary words of parameterizable bit size N.sub.p, coding the sample through a plurality of pairs of values, each pair comprising one of the binary words and an address corresponding to the position of the binary word in the sample, transmitting the pairs of values to an integration unit in order to carry out a MAC operation between the sample and a weighting coefficient.

An in-memory computing method and apparatus, adapted for a processor to perform MAC operations on a memory, are provided. In the method, a format of binary data of weights is transformed from a floating-point format into a quantized format by truncating at least a portion of fraction bits of the binary data and calculating complements of remaining bits, and programming the transformed binary data into cells of the memory. A tuning procedure is performed by iteratively inputting binary data of input signals into the memory, integrating outputs of the memory, and adjusting the weights programmed to the cells based on the integrated outputs. The binary data of the weights is reshaped based on a probability of reducing bits with a value of one in the binary data of each weight. The tuning procedure is repeated until an end condition is met.

An in-memory computing method and apparatus, adapted for a processor to perform MAC operations on a memory, are provided. In the method, a format of binary data of weights is transformed from a floating-point format into a quantized format by truncating at least a portion of fraction bits of the binary data and calculating complements of remaining bits, and programming the transformed binary data into cells of the memory. A tuning procedure is performed by iteratively inputting binary data of input signals into the memory, integrating outputs of the memory, and adjusting the weights programmed to the cells based on the integrated outputs. The binary data of the weights is reshaped based on a probability of reducing bits with a value of one in the binary data of each weight. The tuning procedure is repeated until an end condition is met.

Disclosed herein are systems and methods for converting physical input signals into bitstreams using syntax trees regardless of the physical input signal's protocol. Using declarative language definitions within a protocol declaration, a test and measurement system can compile a syntax tree that automatically translates the input data into a proper bitstream output. The declarative language definitions within the protocol declaration allow custom or standard protocol rules to be written for multiple or arbitrary input protocols without writing unsafe functions, having to access memory, or debugging more complex language codes.

The least-significant-bits (LSBs) of a first data word of a first subset of a first plurality of data words may be compared to the LSBs of each data word of a second subset of a second plurality of data words. The first data word may then be mapped to a second data word of the second subset. A number of LSBs of the second data word matching LSBs of the first data word may be greater than a respective number of LSBs of each data word of a third subset of the second subset matching the LSBs of the first data word, where the third subset excludes the second data word and a most-significant-bit (MSB) of the second data word may be the same as a MSB of the first data word.

The least-significant-bits (LSBs) of a first data word of a first subset of a first plurality of data words may be compared to the LSBs of each data word of a second subset of a second plurality of data words. The first data word may then be mapped to a second data word of the second subset. A number of LSBs of the second data word matching LSBs of the first data word may be greater than a respective number of LSBs of each data word of a third subset of the second subset matching the LSBs of the first data word, where the third subset excludes the second data word and a most-significant-bit (MSB) of the second data word may be the same as a MSB of the first data word.

An encoding system may be provided. The encoding system may comprise a first stage and a second stage. The first stage may be configured to receive a first input, decode the first input, and produce a first output comprising the decoded first input. The second stage may be configured to receive a second input, receive the first output from the first stage, and convert the first input and the second input from a first coding system to a second coding system based on the second input and the first output. The second stage may produce a second output comprising the converted first input and the converted second input.

Because all digital data streams are composed of randomly-distributed zeros (0s) and ones (1s) called bits, it can be posited that all arbitrary-length binary data sets having a finite magnitude can be distilled into numerically-precise integers that accurately represent the value of every individual bit within the set. Mathematically, once a data stream's bit structure has been analyzed, the exact combination of its uniquely-assembled bits, its digital footprint, can be perfectly replicated simply by calculating the numerical value of each consecutive bit to produce a decimal sum equal to the value of the entire stream. This universal data compression technique is called SCALABLE BINARY SUBSTITUTION because the functional objective of the scheme is to analyze the digital footprint of a source data stream, regardless of its magnitude, and substitute the entirety of its encoded information for a simple math expression: Absolutely lossless data compression through mathematically-precise substitution.

Because all digital data streams are composed of randomly-distributed zeros (0s) and ones (1s) called bits, it can be posited that all arbitrary-length binary data sets having a finite magnitude can be distilled into numerically-precise integers that accurately represent the value of every individual bit within the set. Mathematically, once a data stream's bit structure has been analyzed, the exact combination of its uniquely-assembled bits, its digital footprint, can be perfectly replicated simply by calculating the numerical value of each consecutive bit to produce a decimal sum equal to the value of the entire stream. This universal data compression technique is called SCALABLE BINARY SUBSTITUTION because the functional objective of the scheme is to analyze the digital footprint of a source data stream, regardless of its magnitude, and substitute the entirety of its encoded information for a simple math expression: Absolutely lossless data compression through mathematically-precise substitution.

A method for determining a mapping between two code spaces is disclosed. The method may include receiving first and second plurality of data words. The least-significant-bits (LSBs) of a first data word of a first subset of the first plurality of data words may be compared to the LSBs of each data word of a second subset of the second plurality of data words. The first data word may then be mapped to a second data word of the second subset. A number of LSBs of the second data word matching LSBs of the first data word may be greater than a respective number of LSBs of each data word of a third subset of the second subset matching the LSBs of the first data word, where the third subset excludes the second data word and a most-significant-bit (MSB) of the second data word may be the same as a MSB of the first data word.