One of the biggest applications of digital logic is using circuits to perform arithmetical operations. While theoretically, any number system could be used, binary is the most simple to express in terms of digital logic circuits.
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combinational circuit and sequential circuit
Boolean algebra is a mathematical method used to describe the behavior and operation of digital logic. Boolean descriptions and relationships can help us design logic and predict the behavior of more complex digital systems.
Digital logic IS hardware that implements Boolean algebra.
George Boole saw logic as a discipline of mathematics, not as a philosophy. He authored The Laws of Thought and is the inventor of Boolean Logic. Boolean logic was later used in the development of the structure for computer science and how the digital computer came to be formed. Boolean Logic is different from Algebra because it uses true and false variables as opposed to number variables.
Boolean Algebra is the study of the algebra of logic whilst Mathematical logic is a way of applying Boolean algebra. Other applications include set theory, digital logic and probability.