Digital Logic and Basic Concepts Flashcards

Vocabulary practice flashcards covering analog and digital signals, number systems, logic gates, Boolean algebra, arithmetic circuits, multiplexers, decoders, and Karnaugh map minimization.

Amplitude (Analog Signal)

The distance of an analog wave above its reference line.

Cycle

One complete repeating wave of a signal.

Frequency

The number of occurrences or complete wave cycles per second, measured in Hertz ($\text{Hz}$).

Hertz (Hz)

The unit used for expressing signal frequency in cycles per second.

Period ($T$)

The time it takes for a periodic signal to repeat, measured in seconds.

Time High ($t_H$)

The duration of time a digital signal remains at high voltage ($5\,\text{V}$).

Time Low ($t_L$)

The duration of time a digital signal remains at low voltage ($0\,\text{V}$).

Duty Cycle

The ratio of time high ($t_H$) to the total period ($T$), expressed as a percentage: $\text{Duty Cycle} = \frac{t_H}{T} \times 100\%$.

Rising Edge

A $0$-to-$1$ transition of a digital signal.

Falling Edge

A $1$-to-$0$ transition of a digital signal.

Decimal System

A base-10 number system using digits $0$ through $9$ where positional weight increases by powers of ten.

Binary System

A base-2 number system that uses only digits $0$ and $1$, where positional weight increases by powers of two.

Octal System

A base-8 number system composed of eight digits ($0$ through $7$), used as a shorthand for binary values.

Hexadecimal System

A base-16 number system composed of sixteen characters ($0$ through $9$ and $A$ through $F$).

Least Significant Bit (LSB)

The right-most bit in a binary whole number, carrying a positional weight of $2^0 = 1$.

Most Significant Bit (MSB)

The left-most bit in a binary number, whose positional weight depends on the total number of bits.

Logic Gate

An elementary building block of a digital circuit that performs Boolean operations on high ($5\,\text{V}$) and low ($0\,\text{V}$) signals.

AND Gate

A logic gate whose output is $1$ only if all inputs are $1$; otherwise, the output is $0$.

OR Gate

A logic gate whose output is $0$ only if all inputs are $0$; otherwise, the output is $1$.

NOT Gate

A logic gate that accepts a single input signal and outputs its complementary (opposite) value.

NAND Gate

A universal logic gate ("NOT of AND") whose output is $0$ only if all inputs are $1$; otherwise, the output is $1$.

NOR Gate

A universal logic gate ("NOT of OR") whose output is $1$ only if all inputs are $0$; otherwise, the output is $0$.

XOR Gate

An Exclusive-OR logic gate whose output is $0$ when both inputs are identical and $1$ when inputs differ.

XNOR Gate

An Exclusive-NOR logic gate whose output is $1$ when both inputs are identical and $0$ when inputs differ.

Half Adder

A combinational arithmetic circuit that adds two input bits ($A$ and $B$) to produce Sum ($S = A \oplus B$) and Carry ($C = A \cdot B$) outputs.

Full Adder

A combinational arithmetic circuit that adds three input bits ($A$, $B$, and $C_{\text{in}}$) to produce Sum and Carry ($C_{\text{out}}$) outputs.

Multiplexer

A combinational digital switch or data selector with $2^n$ input lines, $1$ output line, and $n$ select lines.

Decoder

A combinational logic circuit with $n$ input lines and $2^n$ output lines that drives a single output high based on input combinations.

Combinational Logic Circuit

A logic circuit without feedback or memory whose outputs are determined strictly by current input values.

Literal

A Boolean variable or its complement (e.g., $a$, $x'$, $z$).

Product Term

A literal or the logical product (AND) of multiple literals (e.g., $ab$, $x'y$).

Sum Term

A literal or the logical sum (OR) of multiple literals (e.g., $a+b$, $x'+y'$).

Sum of Products (SOP)

A Boolean expression formed by the logical OR of multiple product terms.

Product of Sums (POS)

A Boolean expression formed by the logical AND of multiple sum terms.

Minterm

A product of literals in which each input variable appears exactly once, evaluating to true ($1$) for exactly one input combination.

Maxterm

A sum of literals in which each input variable appears exactly once, evaluating to false ($0$) for exactly one input combination.

Canonical Form

A standard form of a switching equation where every term contains all available input variables in either complemented or uncomplemented form.

Don't Care Condition

An input combination marked by $X$ in a truth table where the design output value ($0$ or $1$) does not affect circuit behavior.

Prime Implicant (PI)

A rectangle or group of adjacent minterms on a Karnaugh map that cannot be combined into any larger group.

Essential Prime Implicant (EPI)

A prime implicant that covers at least one minterm not covered by any other prime implicant.

Analog Signal

A time-varying signal that is continuous in both time and amplitude, possessing an infinite range of values.

Digital Signal

A signal that is discrete in time and quantized in amplitude, commonly referred to as a square wave or clock signal with minimum value $0$\,V and maximum value $5$\,V.

Frequency

A measure of the number of signal occurrences or cycles per second, expressed in Hertz ($\text{Hz}$), where $F = \frac{1}{T}$.

Period (T)

The time in seconds ($\text{s}$) required for a periodic signal to complete one wave cycle.

Duty Cycle

The ratio of the time high ($t_H$) to the total period ($T$) of a digital signal, calculated as $\text{Duty Cycle} = \frac{t_H}{T} \times 100\%$.

Rising Edge

A $0\text{-to-}1$ transition of a digital signal.

Falling Edge

A $1\text{-to-}0$ transition of a digital signal.

Least Significant Bit (LSB)

The right-most bit in a binary whole number, carrying a weight of $2^0 = 1$.

Most Significant Bit (MSB)

The left-most bit in a binary number, whose position weight depends on the total bit size of the number.

Octal Number System

A base-8 number system composed of eight digits ($0, 1, 2, 3, 4, 5, 6, 7$).

Hexadecimal Number System

A base-16 number system composed of 16 symbols ($0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ and $\text{A}, \text{B}, \text{C}, \text{D}, \text{E}, \text{F}$).

Logic Gate

An elementary building block of a digital circuit created using transistor technology that performs Boolean operations on high ($5$\,V) and low ($0$\,V) signals.

AND Gate

A basic logic gate where the output is $1$ only when both inputs are $1$; otherwise, the output is $0$ ($X = A \cdot B$).

OR Gate

A basic logic gate where the output is $0$ only when both inputs are $0$; otherwise, the output is $1$ ($X = A + B$).

NOT Gate

A basic logic gate (inverter) that accepts one input signal and returns its complement as output ($X = \bar{A}$).

NAND Gate

A universal logic gate (NOT of AND) where the output is $0$ only when both inputs are $1$; otherwise, the output is $1$ ($X = \overline{A \cdot B}$).

NOR Gate

A universal logic gate (NOT of OR) where the output is $1$ only when both inputs are $0$; otherwise, the output is $0$ ($X = \overline{A + B}$).

XOR Gate

An Exclusive-OR logic gate where the output is $0$ when both inputs are identical, and $1$ when inputs differ ($X = A \oplus B$).

XNOR Gate

An Exclusive-NOR logic gate where the output is $1$ when both inputs are identical, and $0$ when inputs differ ($X = \overline{A \oplus B}$).

DeMorgan's Theorems

Boolean algebra theorems stating that $\overline{A + B} = \bar{A}\bar{B}$ and $\overline{AB} = \bar{A} + \bar{B}$.

Half Adder

A combinational arithmetic circuit that adds two binary input bits ($A$ and $B$) and produces a Sum ($S = A \oplus B$) and a Carry ($C = AB$) output.

Full Adder

A combinational arithmetic circuit that adds three binary bits ($A$, $B$, and $C_{\text{in}}$) and produces a Sum ($\text{Sum} = C_{\text{in}} \oplus (A \oplus B)$) and Carry Out ($C_{\text{out}} = AB + AC_{\text{in}} + BC_{\text{in}}$) output.

Multiplexer (MUX)

A combinational digital switch (data selector) with $2^n$ input lines, $1$ output line, and $n$ select lines that routes a selected input to the output.

Decoder

A combinational circuit that has $n$ inputs and $2^n$ outputs, where a specific output line becomes high ($1$) based on the input binary combination.

Combinational Logic Circuit

A logic circuit without feedback paths or memory elements whose output is strictly a function of its current inputs ($\text{Output} = f(\text{input})$).

Literal

A single Boolean variable or its complement (e.g., $a$, $x'$, or $z$).

Product Term

A single literal or the logical product (AND operation) of multiple literals (e.g., $ab$ or $x'y$).

Sum Term

A single literal or the logical sum (OR operation) of multiple literals (e.g., $a+b$ or $x'+y'$).

Sum of Products (SOP)

A Boolean expression formed by the logical OR of multiple product terms (e.g., $ab + bc' + a'b'$).

Product of Sums (POS)

A Boolean expression formed by the logical AND of multiple sum terms (e.g., $(a+b')(a'+b')$ ).

Minterm

A special product term of literals in an $n$-variable function where each variable appears exactly once, evaluating to $1$ for exactly one combination of inputs.

Maxterm

A special sum term of literals in an $n$-variable function where each variable appears exactly once, evaluating to $0$ for exactly one combination of inputs.

Canonical Form

A standard form of a switching equation in which every term contains all available input variables of the system.

Karnaugh Map (K-Map)

A graphical grid representation of a truth table used to simplify Boolean expressions by grouping adjacent $1$s or $0$s in sizes equal to powers of two ($2^n$).

Don't Care Condition

An input combination marked by $(X)$ in a truth table where the design output value does not matter, allowing flexible grouping in K-maps to simplify equations.

Prime Implicant (PI)

A group of adjacent $1$s on a Karnaugh map that is as large as possible and cannot be combined into a larger group of $2^n$ cells.

Essential Prime Implicant (EPI)

A prime implicant that covers at least one minterm ($1$) on a Karnaugh map that is not covered by any other prime implicant.