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Improving the LUT count for Mealy FSMs with transformation of output collections

Barkalov Alexander, Titarenko Larysa, Mazurkiewicz Małgorzata

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 3

479--494

EN

A method is proposed which aims at reducing the number of LUTs in the circuits of FPGA-based Mealy finite state machines (FSMs) with transformation of collections of outputs into state codes. The reduction is achieved due to the use of two-component state codes. Such an approach allows reducing the number of state variables compared with FSMs based on extended codes. There are exactly three levels of LUTs in the resulting FSM circuit. Each partial function is represented by a single-LUT circuit. The proposed method is illustrated with an example of synthesis. The experiments were conducted using standard benchmarks. They show that the proposed method produces FSM circuits with significantly smaller LUT counts compared with those produced by other investigated methods (Auto and One-hot of Vivado, JEDI, and transformation of output collection codes into extended state codes). The LUT count is decreased by, on average, from 9.86% to 59.64%. The improvement of the LUT count is accompanied by a slightly improved performance. The maximum operating frequency is increased, on average, from 2.74% to 12.93%. The advantages of the proposed method become more pronounced with increasing values of FSM inputs and state variables.

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Improving LUT count of FPGA-based sequential blocks

Barkalov Alexander, Titarenko Larysa, Mazurkiewicz Małgorzata, Krzywicki Kazimierz

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 2

art. no. e136728

EN

Very often, a digital system includes sequential blocks which can be represented using a model of the finite state machine (FSM). It is very important to improve such FSM characteristics as the number of used logic elements, operating frequency and consumed energy. The paper proposes a novel technology-dependant design method targeting LUT-based Mealy FSMs. It belongs to the group of structural decomposition methods. The method is based on encoding the product terms of Boolean functions representing the FSM circuit. To diminish the number of LUTs, a partition of the set of internal states is constructed. It leads to three-level logic circuits of Mealy FSMs. Each function from the first level requires only a single LUT to be implemented. The method of constructing the partition with the minimum amount of classes is proposed. There is given an example of FSM synthesis with the proposed method. The experiments with standard benchmarks were conducted. They show that the proposed method can improve such FSM characteristics as the number of used LUTs. This improvement is accompanied by a decrease in performance. A positive side effect of the proposed method is a reduction in power consumption compared with FSMs obtained with other design methods.

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Improving characteristics of LUT-based Mealy FSMs

Barkalov Alexander, Titarenko Larysa, Mielcarek Kamil

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 4

745--759

EN

Practically, any digital system includes sequential blocks represented using a model of finite state machine (FSM). It is very important to improve such FSM characteristics as the number of logic elements used, operating frequency and consumed energy. The paper proposes a novel technology-dependent design method targeting a decrease in the number of look-up table (LUT) elements and their levels in logic circuits of FPGA-based Mealy FSMs. It produces FSM circuits having three levels of logic blocks. Also, it produces circuits with regular systems of interconnections between the levels of logic. The method is based on dividing the set of internal states into two subsets. Each subset corresponds to a unique part of an FSM circuit. Only a single LUT is required for implementing each function generated by the first part of the circuit. The second part is represented by a multi-level circuit. The proposed method belongs to the group of two-fold state assignment methods. Each internal state is encoded as an element of the set of states and as an element of some of its subsets. A binary state assignment is used for states corresponding to the first part of the FSM circuit. The one-hot assignment is used for states corresponding to the second part. An example of FSM synthesis with the proposed method is shown. The experiments with standard benchmarks are conducted to analyze the efficiency of the proposed method. The results of experiments show that the proposed approach leads to diminishing the number of LUTs in the circuits of rather complex Mealy FSMs having more than 15 internal states. The positive property of this method is a reduction in energy consumption (without any overhead cost) and an increase in operating frequency compared with other investigated methods.

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Hardware reduction for LUT-based mealy FSMs

Barkalov A., Titarenko L., Mielcarek K.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

595--607

EN

A method is proposed targeting a decrease in the number of LUTs in circuits of FPGA-based Mealy FSMs. The method improves hardware consumption for Mealy FSMs with the encoding of collections of output variables. The approach is based on constructing a partition for the set of internal states. Each state has two codes. It diminishes the number of arguments in input memory functions. An example of synthesis is given, along with results of investigations. The method targets rather complex FSMs, having more than 15 states.

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Synteza automatu Moore’a z wbudowanym blokiem pamięci w strukturach programowalnych

Kołopieńczyk M., Barkalov A., Titarenko L.

Pomiary Automatyka Kontrola

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2013

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R. 59, nr 8

776--780

PL

W artykule zostanie przedstawiona metoda umożliwiająca syntezę skończonego automatu stanów typu Moore’a z wbudowanym blokiem pamięci (ang. Embedded Memory Blocks, EMB) w strukturach programowalnych typu FPGA (ang. Field Programmable Gate Array, FPGA). Zaproponowana metoda bazuje na kodowaniu pewnej wybranej części zbioru warunków logicznych przez dodatkowe zmienne. W artykule zostanie zaprezentowany przykład projektowania układu.

EN

The model of the Moore finite state machine (FSM) is very often used for representing a control unit [1]. Nowadays, two classes of programmable logic devices: complex programmable logic devices (CPLD) and field-programmable gate arrays (FPGA) are used for implementing logic circuits of FSMs [2, 3]. This paper deals with FPGA-based Moore FSMs. It is very important to use EMBs in the logic design. It leads to decreasing in both the number of interconnections and chip area occupied by an FSM logic circuit. In turn, it results in decrease in the propagation time as well as the consumed power of a circuit [9]. A lot of methods for implementing an FSM logic circuit with RAMs are known [10 – 19]. For rather complex FSMs, the method of replacement of logical conditions [20] is used. In this case, optimization efforts target hardware reduction for the multiplexer executing the replacement. In this paper we propose a method based on existence of pseudoequivalent states of the Moore FSM for solving this problem [21]. The method is based on replacement of some part of the set of logical conditions by additional variables. It results in diminishing the number of LUTs in the multiplexer used for replacement of logical conditions. To represent a control algorithm, the language of graph-schemes of algorithms [20] is used. An example of application of the proposed design method is given.