STUDY OF THE MULTI-INPUT LUT COMPLEXITY
DOI:
https://doi.org/10.15588/1607-3274-2018-1-2Keywords:
logic element, FPGA, LUT, transistor, adaptive logic module, decomposition, complexity, speed.Abstract
Сontex. The programmable logic integrated circuits FPGA (field-programmable gate array) used realization of the generator offunctions LUT (Look Up Table), which is configured by loading a configuration memory for calculating a logic function in perfect
disjunctive normal form (PDNF). The LUT dimension determines the technological limitations of Mead and Conway on the number of
series-connected MOS transistors. The standard number of LUT inputs for many years was 3 or 4, and 4-LUT is constructed from two 3-
LUTs with an additional 1-LUT. However, in many projects, it is required to calculate functions of a large number of arguments. This
requires a multi-input LUT, which is built as a decomposition of 3-LUT, 4-LUT. The speed of computing logic functions determines by the
delay in the coupling matrices, so this decomposition leads to a decrease in performance. In recent years, the direction of adaptive logical
modules (ALM) has been actively developing, in which the user has access to various versions of logical elements for five, six and even
seven, eight variables, which leads to an increase in performance. However, the manufacturer’s documentation does not provide a detailed
description of the features of such multi-input LUTs, taking into account the Meade-Conway constraints. In addition, there are no estimates
of complexity and speed of multi-input LUTs. The analysis of sources allows suggests a further increase in the LUT bit capacity and the
convergence of FPGA and CPLD (complex programmable logic devices) capabilities in terms of bit depth. Therefore, studies of the features
of constructing multi-input LUTs are relevant and the authors attempted to analyze the implementation of such prospective multi-bit logic
Objective. The purpose of this work is to estimate the complexity and speed of the decomposition of a multi-bit LUT.
Method. Obtaining expressions for estimating the complexity and speed of decomposition of a multi-bit LUT on a LUT of a lower bit
length.
Results. A comparison of the complexity and delay in the number of transistors in the decomposition of a multi-bit LUT in the
computer mathematics system Mathcad is performed.
Conclusions. The conducted researches made it possible to establish the features of constructing multi-bit LUTs and to evaluate
various variants of decomposition with further increase in the LUT dimension with the subsequent choice of the optimal ALM variant.
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