Minimal Realizations of Logic Functions Using Truth Table Method with Distributed Simplification

Abstract

In the conventional method, a truth table (TT) is prepared from the specified logic function. Then it is expressed as the sum of min terms corresponding to the rows in which 1 appears. Finally, this function is further reduced using the Boolean identities. Thus, all the simplifications are concentrated at one place after the TT. This procedure does not always lead to the minimal realization. This paper deals with the minimal realization of logic function using TT in which TT is reduced successively by one variable at a time till all the variables are exhausted. The simplification is carried out, instead at the end of the truth table, at the end of each step of TT reduction. The method is shown to be systematic, and definitely leads to the minimal function. It is simpler in operation than that based on only Boolean identities, Karnaugh map and Quine-McClusky methods, and can handle any number of variables. It is explained with several examples. It is worth introducing as an improvement over the classical TT method in class room teaching.

Research of 5-bit boolean functions minimization protocols by combinatorial method

“…Minimization protocols for the 5-bit Boolean functions of the combinatorial method make up a protocol library for the process of minimizing 5 ISSN 2226-3780 standard procedures, so the application of a separate protocol is reduced to carrying out one algebraic transformation.…”

Minimization of Boolean functions by combinatorial method

“…In contrast to [7][8][9][10][11][12][13][14][15][16], in this paper, the object of solving the problem of minimizing a Boolean function is a combinatorial block-diagram with repetition, which allows to concentrate the minimization principle within the truth table of a given function. The peculiarities of the combinatorial method consist in greater informativeness of the process of solving the problem in comparison with the algebraic method of minimizing the function, due to tabular organization and the introduction of figurative calculus apparatus.…”

“…The second option is to minimize the 5-bit logic function (9). At the first stage, sets of three blocks are identified that allow procedures for gluing and replacing of variables.…”

“…No. Using Table 5, let's compose the PDNF of the given 5-bit function from the blocks for which the function receives the value of 1, that is, for the sets 1,4,5,7,9,11,12,13,16,17,18,22,28,31. …”

“…In [9], a simple and systematic method for minimizing a logical function is proposed. The method consists in reducing the truth table from N variables N-1, N -from 1 to N-2, and so on in a sequence until all variables are exhausted with built-in all possible simplifications, after each reduction.…”