Boolean Algebra
In the tutorial about the Sum-of-Product (SOP) expression, we saw that it represents a standard Boolean (switching) expression which “Sums” two or more “Products” by taking the output from two or more logic AND gates and OR’s them together to create the final output. But we can also take the outputs of two or more OR gates and…
Switching Theory allows us to understand the operation and relationship between Boolean Algebra and two-level logic functions with regards to Digital Logic Gates. Switching theory can be used to further develop the theoretical knowledge and concepts of digital circuits when viewed as an interconnection of input elements producing an output state…
Boolean Algebra is a simple and effective way of representing the switching action of standard logic gates and a set of rules or laws have been invented to help reduce the number of logic gates needed to perform a particular logical operation. Boolean Algebra is the digital logic mathematics we…
As we have seen previously, Boolean Algebra uses a set of laws and rules to define the operation of a digital logic circuit with “0’s” and “1’s” being used to represent a digital input or output condition. Boolean Algebra uses these zeros and ones to create truth tables and mathematical…
Boolean Algebra and the Laws of Boolean Algebra can be used to identify unnecessary logic gates within a digital logic design reducing the number of gates required saving on power consumption and cost. We have seen throughout this section that digital logic functions can be defined and displayed as either…
As well as a standard Boolean Expression, the input and output information of any Logic Gate or circuit can be plotted into a standard table to give a visual representation of the switching function of the system. The table used to represent the boolean expression of a logic gate function is commonly…
As well as the logic symbols “0” and “1” being used to represent a digital input or output, we can also use them as constants for a permanently “Open” or “Closed” circuit or contact respectively. A set of rules or Laws of Boolean Algebra expressions have been invented to help…
The NOR or “Not OR” gate is also a combination of two separate logic functions, Not and OR connected together to form a single logic function which is the same as the OR function except that the output is inverted. To create a NOR gate, the OR function and the NOT function are connected…
The NAND or “Not AND” function is a combination of the two separate logical functions, the AND function and the NOT function in series. The logic NAND function can be expressed by the Boolean expression of, A.B The Logic NAND Function will not produce an output when “ALL” of its inputs are present…
The Logic NOT Function is simply a single input inverter that changes the input of a logic level “1” to an output of logic level “0” and vice versa. The “logic NOT function” is so called because its output state is NOT the same as its input state with its Boolean Expression generally denoted…
The Logic OR Function function states that an output action will become TRUE if either one “OR” more events are TRUE, but the order at which they occur is unimportant as it does not affect the final result. For example, A + B = B + A. In Boolean algebra the Logic OR…
In 1854, George Boole performed an investigation into the “laws of thought” which were based around a simplified version of the “group” or “set” theory, and from this Boolean Algebra was developed. Boolean Algebra deals mainly with the theory that both logic and set operations are either “TRUE” or “FALSE” but not both…