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Let's start this tutorial with some basics of SOP form and NOR gates before getting into the details of how to realize a logic function or Boolean expression in SOP form using NOR gates only. SOP Form SOP form stands for Sum of Products form. SOP form is one in which a Boolean expression is expressed as a sum of product terms. For example, $$\mathrm{\mathit{f}\lgroup A, B, C\rgroup=AB+ABC+B\overline{C}}$$ This is a Boolean function expressed in SOP (Sum of Products) form. NOR Gate NOR Gate is a universal logic gate, i.e., NOR gate can be used for realization of any ... Read More
SOP Form SOP form stands for Sum of Products form. SOP form is one in which a Boolean expression is expressed as a sum of product terms. For example, $$\mathrm{\mathit{f}\lgroup A, B, C\rgroup=AB+ABC+B\overline{C}}$$ This is a Boolean function expressed in SOP (Sum of Products) form. NAND Gate The NAND Gate is a type of universal logic gate. It is a logic gate one that can be used to realize any kind of logical function or any other type of logic gate. A NAND gate is basically a combination of two basic logic gates namely AND gate and NOT gate, i.e. ... Read More
In positional number systems, the radix is the total number of unique digits that are used to represent numbers in that number system. Radix is also called Base. For example, in decimal number system, we use total ten digits from 0 to 9 (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent any decimal number. Therefore, for the decimal number system, the radix or base is ten (10). Although we can easily convert a given number from one radix (i.e. number system) to any other radix (number system) by using radix conversion protocols. In this article, ... Read More
Otto Cycle An air standard cycle called the Otto Cycle is employed in spark ignition (SI) engines. It comprises of two reversible adiabatic processes and two isochoric processes (constant volume), totaling four processes. When the work interactions take place in reversible adiabatic processes, the heat addition (2-3) and rejection (4-1) occur isochorically (3-4 and 1-2). The Otto cycle's schematic is shown in Figure given below. To model the cycle in Python, the input variables considered are maximum pressure $\mathrm{(P_{max})}$, minimum pressure $\mathrm{(P_{min})}$, maximum volume $\mathrm{(V_{max})}$, compression ratio (r), and adiabatic exponent $\mathrm{(\gamma)}$. Table 2 explains the thermodynamic computations of ... Read More
The K-Map or Karnaugh Map is a systematic method of simplifying a complex Boolean function or expression. The K-Map is basically a graph or a chart which consists of a certain number of adjacent cells. Each cell represents a particular combination of variables in either sum or product form. However, we can use the K-Map for simplifying a Boolean function in any number of variables, but it becomes tedious for functions involving five or more variables. In actual practice, we usually use K-Map for simplification of Boolean functions in upto six variables. A Boolean function in n variables can have ... Read More
Gauss Seidel Method is the iterative method to solve any system of linear equations. Though the method is very much similar to the Jacobi's method but the values of unknown (x) obtained in an iteration are used in the same iteration in Gauss Seidel whereas, in Jacobi's method they are used in the next iteration level. The updation of x in the same step speeds up the convergence rate. A system of liner equation can be written as − $$\mathrm{a_{1, 1}x_{1} \: + \: a_{1, 2}x_{2} \: + \: \dotso \: + \: a_{1, n}x_{n} \: = \: b_{1}}$$ $$\mathrm{a_{2, ... Read More
Any Boolean function or logical expression can be expressed in either canonical/standard sum of products form or canonical/standard product of sums form. The standard sum of products form of a logical expression contains different product terms which are added together, and each product term is referred to as a minterm. On the other hand, the standard product of sums form of a logical expression contains different sum terms which are multiplied together, and each sum term is called a maxterm. In this article, we will discuss about the minterm and max terms. What is Minterm? When a Boolean function or ... Read More
When an object at very high temperature is suddenly dropped in a cooler liquid and if it is assumed that the conductive resistance of the solid is very small in comparison to the surrounding convective resistance then the heat transfer analysis is called as lumped capacitance analysis (as shown in the figure given below). Here, we treat the system as a lump. In that case, we can assume that the rate of change of internal energy of lump will be equal to the heat interaction with the surrounding fluid. Mathematically, this can be written as − $$\mathrm{pcV\frac{\partial T}{\partial t} ... Read More
Before focusing on logical expression in SSOP (Standard Sum of Products) form and SPOS (Standard Product of Sum) form, let us have a brief introduction the "Sum of Products" and "Product of Sum" forms. SOP (Sum of Products) Form The SOP or Sum of Products form is a form of expressing a logical or Boolean expression. In SOP, different product terms of input variables are logically ORed together. Therefore, in the case of SOP form, we first logically AND the input variables, and then all these product terms are summed together with the help of logical OR operation. For example ... Read More
Electronic logic conventions are the sets of rules followed while designing a digital logic system or device. These conventions are adopted due to their different characteristics observed by several experiments. The use of electronic logic conventions, makes the implementation process of a digit system easy and smooth. Also, a standardization is achieved in the design. This tutorial is entirely meant for explaining different electronic logic conventions used in digital system implementations. As we know, the digital systems are implemented in binary number system due to some technical and economic reasons. The binary number system follows Boolean’s rules to perform arithmetic ... Read More