Binary is the foundation of computer systems, using only 0s and 1s to represent data. These two states correspond to the on and off states of a computer's electrical circuits. Every operation in a computer ultimately breaks down into binary computations.
Boolean functions use logical expressions to represent true (1) or false (0) values. These functions are fundamental in digital computing, where they govern operations like addition, data comparison, and control flow.
Combinatorial circuits are built using Boolean functions and consist of logic gates like AND, OR, NOT, NAND, and NOR. Unlike sequential circuits, combinatorial circuits don't rely on memory; their output depends solely on the current inputs.
Logical operators like AND, OR, NOT, and XOR are applied to solve problems in mathematical logic. These operators form the basis of decision-making in applied computing and programming
Understand how Boolean functions are used to design combinatorial circuits. These circuits represent logical operations in hardware, forming the backbone of computing devices.
Mathematical sets and their operations, including union, intersection, and difference. Sets are crucial for solving problems involving discrete objects in applied computing.
Modular arithmetic is applied to solve practical problems in programming and cryptography, such as hashing, cyclic counters, and time calculations.
Use graph models to solve problems involving relationships between discrete objects, such as shortest paths, network optimization, and scheduling tasks.