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Introduction
Published in Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski, Computer Arithmetics for Nanoelectronics, 2018
Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski
Boolean functions are particular functions that can be described in terms of expressions over Boolean algebra, called Boolean formulas. A Boolean formula of n variables is a string of symbols of x1,x2,…,xn, the binary operations of Boolean sum (∨), Boolean product (⋅), unary operation of the complement (-), and brackets (). A Boolean formula is the Boolean function after specification of values, given assignments of variables.
Boolean Algebra
Published in Sasho Andonov, Bowtie Methodology, 2017
As I have already mentioned, the logic of Boolean functions can be presented as an electronic circuit. Sometimes logic tells us that there are different circuits (Boolean functions) which present same outputs for same inputs. These are called equivalent functions. There are plenty of situations when different circuits produce the same outputs when the inputs are the same and even though these circuits are not the same, we call them equivalent circuits. In Figure 4.2, you can see two equivalent circuits with their Truth tables. You can notice that the circuits are quite different because they use different elements, but they are equivalent because the input is the same as the output. These two circuits actually present the first De Morgan’s theorem from Table 4.3.
Logic Design Fundamentals
Published in Joseph Cavanagh, Computer Arithmetic and Verilog HDL Fundamentals, 2017
This section will present various techniques for minimizing a Boolean function. A Boolean function is an algebraic representation of digital logic. Each term in an expression represents a logic gate and each variable in a term represents an input to a logic gate. It is important, therefore, to have the fewest number of terms in a Boolean equation and the fewest number of variables in each term. A Boolean equation with a minimal number of terms and variables reduces not only the number of logic gates, but also the delay required to generate the function.
Petri net models for Physarum machines built to realise Boolean functions
Published in International Journal of Parallel, Emergent and Distributed Systems, 2018
Boolean functions are a powerful mathematical tool used in different areas of electronics and computer science, e.g. for designing digital circuits, computer systems, control systems, reasoning systems, etc. In general, they describe relationships between entities with binary states. The theory of Boolean functions is well established. Each Boolean function can be written in one of its two canonical forms, a disjunctive canonical form or a conjunctive canonical form. Both of canonical forms are equivalent. Moreover, each canonical form can be minimised to simplify a device realising a Boolean function. Basics of Boolean functions are briefly recalled in Section 2.1.