Digital Logic Circuits

•          Digital Logic Circuits

–        Digital Logic Circuit is a basic electronic component of a digital system

–        Values of digital signals are 0 or 1 (bits)

–        Black Box is specified by the signal input/output table

–        Three gates: NOT-gate, AND-gate, OR-gate

–        Combinational circuit is a combination of logical gates

–        Combinational circuit always correspond to some boolean expression, such that input/output table of a table and a truth table of the expression are identical

–        A recognizer is a circuit that outputs 1 for exactly one particular combination of input signals and outputs 0’s for all other combinations

–        Multiple-input AND and OR gates

–        Finding a circuit that corresponds to a given input/output table:

•          Construct equivalent boolean expression using disjunctive normal form: for all outputs of 1 construct a conjunctive form based on the truth table row. All conjunctive forms are united using disjunction

•          Construct a digital logic circuit equivalent to the boolean expression

–        Design a circuit for the following output: (0, 0, 1, 1, 0, 0, 1, 0)

–        Two digital logic circuits are equivalent iff their input/output tables are identical

–        Simplification of circuits

–        Scheffer stroke (NAND)

–        Peirce arrow (NOR)