Digital Logic: Binary Logic, Truth Tables, and Logic Gates

This set of vocabulary flashcards covers the fundamental concepts of binary logic, electronic signal representation, basic logic operations (AND, OR, NOT), and the various digital logic gates including NAND, NOR, XOR, and XNOR.

Binary Logic Variables

Variables that can only have a value of 0 or 1, representing states such as (yes, no), (true, false), or (on, off).

Electronic Logic 1

A high voltage level used to represent a logical 1; in the provided example, this range is $3V$ to $4V$.

Electronic Logic 0

A low voltage level used to represent a logical 0; in the provided example, this range is $0V$ to $1V$.

AND Operation

A logical operation where the output $z=1$ if and only if all inputs are 1; otherwise, $z=0$. Represented as $x \cdot y = z$ or $xy = z$.

OR Operation

A logical operation where the output $z=1$ if at least one input is 1; if all inputs are 0, then $z=0$. Represented as $x + y = z$.

NOT Operation

Also known as the complement; it changes a 1 to a 0 and a 0 to a 1. Represented as $x'$ or $\overline{x}$.

Truth Table

A table that shows all possible combinations of the inputs and gives the corresponding outputs.

Logic Gate

An electronic circuit that operates on one or more input signals to produce an output signal.

Inverter

Another name for a NOT gate, which produces the complement of its input signal.

Buffer

A logic gate that produces an output signal equal to its input signal ($F = x$).

NAND Gate

A logic gate that performs the complement of the AND operation, defined by the expression $F = (xy)'$.

NOR Gate

A logic gate that performs the complement of the OR operation, defined by the expression $F = (x + y)'$.

Exclusive-OR (XOR)

A logic gate where the output is 1 if the inputs are different and 0 if the inputs are the same.

Exclusive-NOR (XNOR)

Also known as equivalence, this gate produces a 1 if the inputs are the same and a 0 if they are different.

Logic vs. Arithmetic (OR)

While arithmetic states $1 + 1 = 2$, binary logic states $1 + 1 = 1$ (one OR one is equal to one).