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Binary Logic
A form of logic that operates on binary values (0 and 1), used in digital circuits and computer systems to represent and manipulate data.
Logic Gate
An electronic component that implements a Boolean function, processing one or more binary inputs to produce a single binary output.
Truth Table
A table that summarizes the output of a Boolean function for all possible combinations of its inputs, showing how the output varies with different input values.
AND
A basic logic gate that outputs true (1) only when all its inputs are true (1).
OR
A basic logic gate that outputs true (1) when at least one of its inputs is true (1).
NOT
A basic logic gate that outputs true (1) when its input is false (0), and false (0) when its input is true (1).
XOR
A logic gate that outputs true (1) only when the number of true inputs is odd, typically true when exactly one input is true.
De Morgan’s Laws
Two rules in Boolean algebra that relate conjunctions and disjunctions of variables through negation. They state that the negation of a conjunction is equivalent to the disjunction of the negations, and vice versa so any integrated circuit can be built from just one type of logic gate (NAND or NOR).
De Morgan’s first law
The negation of a disjunction is equivalent to the conjunction of the negations, expressed as ¬(A ∨ B) = ¬A ∧ ¬B.
De Morgan’s second law
The negation of a conjunction is equivalent to the disjunction of the negations, expressed as ¬(A ∧ B) = ¬A ∨ ¬B.
Associative rule
In Boolean algebra, the associative rule states that the grouping of variables does not affect the result of conjunction or disjunction operations. It can be expressed as (A ∧ B) ∧ C = A ∧ (B ∧ C) and (A ∨ B) ∨ C = A ∨ (B ∨ C).
Distributive rule
In Boolean algebra, the distributive rule states that conjunction distributes over disjunction and vice versa. It can be expressed as A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C) and A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C).
Absorption rule
In Boolean algebra, the absorption rule states that a variable can absorb a conjunction or disjunction with itself, expressed as A ∨ (A ∧ B) = A and A ∧ (A ∨ B) = A.
Double negation
In Boolean algebra, the double negation rule states that negating a variable twice yields the original variable, expressed as ¬(¬A) = A.
Karnaugh map
A graphical method used to simplify Boolean expressions by organizing truth values into a grid format, allowing for easy identification of common factors and minimization of logic functions.
Half adder
A digital circuit that computes the sum of two bits and produces a sum and a carry output. It has two inputs and two outputs, typically referred to as the sum (S) and carry (C).
Full adder
A digital circuit that computes the sum of three binary bits, typically two significant bits and a carry bit from a previous addition, producing a sum and a carry output.
D-type flip-flop
An edge-triggered flip-flop. A digital memory circuit that captures the value of the input data line (0 or 1) at the beginning of a clock period, maintaining that value until the next clock signal. It has two stable states and is used for data storage and transfer in sequential circuits.
Flip-flop
A basic digital memory circuit that can hold one bit of data. It has two stable states, 0 and 1, and is commonly used in sequential logic circuits. It has two inputs, a control input labelled D and a clock signal.
Register memory
Constructed by connecting multiple flip-flops together, allowing for the storage and manipulation of multiple bits of data simultaneously. Registers are used in CPUs for temporary data storage and processing.
