2,204 research outputs found
Weighted p-bits for FPGA implementation of probabilistic circuits
Probabilistic spin logic (PSL) is a recently proposed computing paradigm
based on unstable stochastic units called probabilistic bits (p-bits) that can
be correlated to form probabilistic circuits (p-circuits). These p-circuits can
be used to solve problems of optimization, inference and also to implement
precise Boolean functions in an "inverted" mode, where a given Boolean circuit
can operate in reverse to find the input combinations that are consistent with
a given output. In this paper we present a scalable FPGA implementation of such
invertible p-circuits. We implement a "weighted" p-bit that combines stochastic
units with localized memory structures. We also present a generalized tile of
weighted p-bits to which a large class of problems beyond invertible Boolean
logic can be mapped, and how invertibility can be applied to interesting
problems such as the NP-complete Subset Sum Problem by solving a small instance
of this problem in hardware
Modified Level Restorers Using Current Sink and Current Source Inverter Structures for BBL-PT Full Adder
Full adder is an essential component for the design and development of all types of processors like digital signal processors (DSP), microprocessors etc. In most of these systems adder lies in the critical path that affects the overall speed of the system. So enhancing the performance of the 1-bit full adder cell is a significant goal. In this paper, we proposed two modified level restorers using current sink and current source inverter structures for branch-based logic and pass-transistor (BBL-PT) full adder [1]. In BBL-PT full adder, there lies a drawback i.e. voltage step existence that could be eliminated in the proposed logics by using the current sink inverter and current source inverter structures. The proposed full adders are compared with the two standard and well-known logic styles, i.e. conventional static CMOS logic and Complementary Pass transistor Logic (CPL), demonstrated the good delay performance. The implementation of 8-bit ripple carry adder based on proposed full adders are finally demonstrated. The CPL 8-bit RCA and as well as the proposed ones is having better delay performance than the static CMOS and BBL-PT 8-bit RCA. The performance of the proposed BBL-PT cell with current sink & current source inverter structures are examined using PSPICE and the model parameters of a 0.13 µm CMOS process
Hardware emulation of stochastic p-bits for invertible logic
The common feature of nearly all logic and memory devices is that they make
use of stable units to represent 0's and 1's. A completely different paradigm
is based on three-terminal stochastic units which could be called "p-bits",
where the output is a random telegraphic signal continuously fluctuating
between 0 and 1 with a tunable mean. p-bits can be interconnected to receive
weighted contributions from others in a network, and these weighted
contributions can be chosen to not only solve problems of optimization and
inference but also to implement precise Boolean functions in an inverted mode.
This inverted operation of Boolean gates is particularly striking: They provide
inputs consistent to a given output along with unique outputs to a given set of
inputs. The existing demonstrations of accurate invertible logic are
intriguing, but will these striking properties observed in computer simulations
carry over to hardware implementations? This paper uses individual micro
controllers to emulate p-bits, and we present results for a 4-bit ripple carry
adder with 48 p-bits and a 4-bit multiplier with 46 p-bits working in inverted
mode as a factorizer. Our results constitute a first step towards implementing
p-bits with nano devices, like stochastic Magnetic Tunnel Junctions
On decoding of multi-level MPSK modulation codes
The decoding problem of multi-level block modulation codes is investigated. The hardware design of soft-decision Viterbi decoder for some short length 8-PSK block modulation codes is presented. An effective way to reduce the hardware complexity of the decoder by reducing the branch metric and path metric, using a non-uniform floating-point to integer mapping scheme, is proposed and discussed. The simulation results of the design are presented. The multi-stage decoding (MSD) of multi-level modulation codes is also investigated. The cases of soft-decision and hard-decision MSD are considered and their performance are evaluated for several codes of different lengths and different minimum squared Euclidean distances. It is shown that the soft-decision MSD reduces the decoding complexity drastically and it is suboptimum. The hard-decision MSD further simplifies the decoding while still maintaining a reasonable coding gain over the uncoded system, if the component codes are chosen properly. Finally, some basic 3-level 8-PSK modulation codes using BCH codes as component codes are constructed and their coding gains are found for hard decision multistage decoding
Arithmetic Operations in Multi-Valued Logic
This paper presents arithmetic operations like addition, subtraction and
multiplications in Modulo-4 arithmetic, and also addition, multiplication in
Galois field, using multi-valued logic (MVL). Quaternary to binary and binary
to quaternary converters are designed using down literal circuits. Negation in
modular arithmetic is designed with only one gate. Logic design of each
operation is achieved by reducing the terms using Karnaugh diagrams, keeping
minimum number of gates and depth of net in to consideration. Quaternary
multiplier circuit is proposed to achieve required optimization. Simulation
result of each operation is shown separately using Hspice.Comment: 12 Pages, VLSICS Journal 201
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