Digital Fundamentals

A set of vocabulary flashcards covering the fundamental concepts of digital electronics, logic gates, number systems, and arithmetic circuits based on the Chapter 41 lecture notes.

bit

A single binary character, either $0$ or $1$.

nibble

A pattern consisting of $4$ bits.

byte

A group of $8$ bits that may represent a decimal number from $0$ to $255$.

word

A number of bits in sequence that are treated as a single unit, typically in sizes of $8$, $16$, $32$, or $64$ bits.

least significant bit (LSB)

The digit in a binary number that represents the least value.

most significant bit (MSB)

The digit in a binary number that represents the greatest value.

binary number system

A $\text{base-two}$ system that uses only the digits $0$ and $1$ to represent numbers.

hexadecimal

A numbering system with a $\text{base 16}$ that employs $16$ digits, specifically the numbers $0$ through $9$ and the letters $A$ through $F$.

gate

An electric circuit that operates on the yes-no principle and produces an output only when predetermined input conditions exist.

AND gate

A logic device with two or more inputs and one output where all inputs must be in the logic $1$ (HIGH) state to obtain a logic $1$ output.

OR gate

A decision-making circuit with two or more inputs and one output whose output is logic $0$ (LOW) unless any or all of its inputs are logic $1$ (HIGH).

NOT (inverter) gate

A logic gate that takes a single input and reverses or complements its logic state.

NAND gate

A universal logic gate that is a combination of an AND gate and an INVERTER, with an output exactly opposite that of an AND gate.

NOR gate

A combination of an OR gate and an INVERTER, with an output exactly opposite that of an OR gate.

TTL

Short for transistor-transistor logic, a digital IC family based on the use of multiple bipolar transistor circuits operating at $5\,V_{cc}$.

CMOS

An abbreviation for Complimentary Metal Oxide Semiconductor, a logic gate type that uses FETs (Field Effect Transistors) and operates at $3$ to $18\,volts$.

combinational logic

Logic circuits that make decisions based on inputs without any internal storage or memory.

Boolean algebra

A mathematical method used to express logical operations where the multiplication sign represents AND, the addition sign ($+$) represents OR, and a bar over a letter represents NOT.

exclusive-OR (XOR)

A logic function where the output is HIGH only when one input or the other is HIGH, but not both.

fan-out

A number describing the limit of how many inputs to other gates a single logic circuit output can drive, typically ranging from $3$–$10$ for standard gates.

arithmetic-logic unit (ALU)

The heart of a computer that performs all mathematical operations, including addition, subtraction, multiplication, and division.

half-adder

A logic circuit with two inputs ($A$, $B$) and two outputs serving as a sum ($\Sigma$) and a carry out ($C_o$).

full-adder

A logic circuit that has the capability to add two bits and a carry in ($C_{IN}$) from a previous addition.

asynchronous device

A device, such as the $7485$ magnitude comparator, that operates only when inputs are applied or changed and is not controlled by a clock.

encoder

A combinational network of gates that converts a nonbinary input into a binary digital code.

decoder

A combinational logic circuit that recognizes the presence of a specific binary number or converts binary data into a format like a seven-segment decimal display.

multiplexer (MUX)

Also called a data selector, this electronic switch allows digital information from several sources to be routed onto a single line for transmission.

demultiplexer (DEMUX)

A digital circuit that performs the inverse operation of a multiplexer by taking a single input and routing it to one of several outputs.

DeMorgan's Law

A fundamental result of Boolean algebra showing that logical functions can be implemented using either AND gates and inverters ($\overline{AB} = \bar{A} + \bar{B}$) or OR gates and inverters ($\overline{A+B} = \bar{A}\bar{B}$).