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Boolean algebra is a mathematical framework that deals with binary variables and logical operations. It is applied extensively in the field of digital electronics to design and simplify logical expressions and circuits. In Boolean algebra, the variables can only take two values, typically represented as 0 and 1, which stands for false and true, respectively.

The fundamental logical operations in Boolean algebra are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Each operation has a corresponding Boolean expression and can be represented visually by a logic gate in digital circuits. The primary reason for using Boolean algebra in digital logic design is its ability to provide a systematic approach for representing complex logical relationships and simplifying them into minimal expressions through a series of laws and properties such as De Morgan's Theorems.

Digital logic is the foundation of digital systems found in computers, mobile phones, and many other modern devices. It involves processing binary information, where the logic levels are defined as '0' (low) or '1' (high). These levels correspond to different voltage ranges in physical circuits.

Digital logic utilizes a series of gates that perform basic logical functions on one or more input signals to produce a single output. The NOR gate, as featured in our exercise, is a universal gate, which means any other logic function can be constructed using just NOR gates. This is valuable in the design of integrated circuits as it allows for more standardized and streamlined manufacturing processes.

Digital logic designs are often validated using truth tables that enumerate output states for every possible combination of input states, which helps in understanding and debugging complex logic circuits.

Truth tables are a tabular representation of all possible scenarios and outcomes for a logical operation or circuit. Each row of the table corresponds to a unique combination of input values, and the column(s) depict the resulting output(s) for each input scenario.

The truth table for the NOR gate, which combines the functions of the NOT and OR gates, reflects that the output is true only when both inputs are false. This is visually represented in the step-by-step solution's logic table:\begin{center} \[\begin{tabular}{|c|c||c|} \hline A & B & Output \ \hline 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 0 & 0 \ 1 & 1 & 0 \ \hline \end{tabular}\]By interpreting truth tables, students and engineers alike can deduce the behavior of any given digital logic circuit. They are an essential tool for both learning and design processes of digital electronics.