In discrete mathematics, a relation is antisymmetric if no two distinct elements are related to each other in both directions simultaneously.

Antisymmetric Relation

Discrete Math

Convert any base to another with this tool!

Number Base Converter

Computer Organization

Any Base Math in computer organization refers to the system of counting in different numerical bases, such as binary (base 2), decimal (base 10), etc.

Any Base Math Calculator

Arithmetic sequences in discrete math are a series of numbers where each term is incremented by a constant value from the previous term.

Arithmetic Sequence

An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant, known as the common difference.

Arithmetic Series

An asymmetric relation is a binary relation where if (a, b) is in the relation, then (b, a) is not in the relation for all a ≠ b.

Asymmetric Relation

Calculate the mean, median, mode, range, minimium, maximum, midrange, sum, count, and element frequency of a numerical data set!

Mean, Median, Mode, Range Calculator

statistics

Bayes' Theorem calculates the probability of an event based on prior knowledge of conditions related to the event.

Bayes' Theorem

Bernoulli Trials are experiments with two possible outcomes, success or failure, repeated independently under identical conditions.

Bernoulli Trials

Bijective functions establish one-to-one correspondence between sets, ensuring each element has a unique mapping and a unique inverse function.

Bijective Functions

A BCD Converter is a tool in computer organization that translates decimal numbers into binary coded decimal format, aiding in data processing.

Binary Coded Decimal (BCD) Converter

Binary conversions involve translating numbers from decimal, hexadecimal, or octal systems into binary (base 2) used in computer systems.

Binary Conversions

Binary math in computer organization involves operations on binary numbers (0s and 1s), which are the fundamental building blocks of computer systems.

Binary Math Calculator

A Binary Translator converts binary code into human-readable text or instructions, aiding in understanding and debugging computer systems.

ASCII Binary Translator

Explore the concept of bitwise AND in computer architecture. Learn its applications in low-level data manipulation, hardware optimization, and bitwise logic operations.

Bitwise AND Calculator

computer-organization

Explore the concept of bitwise complement in computer architecture. Learn how it facilitates bit inversion, bitwise operations, and data manipulation at the binary level.

Bitwise Complement (NOT) Calculator

Discover the concept of bitwise OR in computer programming. Explore its applications in merging data, setting flags, and performing logical operations at the bit level.

Bitwise OR Calculator

Explore the concept of bitwise XOR in computer programming. Learn how it facilitates flipping bits, toggling flags, and performing exclusive logical operations at the bit level.

Bitwise XOR Calculator

A bipartite graph is a graph whose vertices can be partitioned into two disjoint sets such that no two vertices in the same set are adjacent.

Bipartite Graph

Bit Shift is a bitwise operation that moves binary digits left or right, effectively multiplying or dividing the number by powers of two.

Bit Shift

Bitwise NAND is a binary operation that takes two equal-length bit patterns and performs a logical NAND operation on each pair of corresponding bits.

Bitwise NAND

Bitwise NOR is a binary operation that applies the logical NOR operator to each pair of bits. It returns 1 only if both bits are 0.

Bitwise NOR

Discover the concept of bit rotation in computer programming. Learn how it enables efficient data reordering, circular buffer implementation, and bitwise shifting of binary values.

Bit Rotation

Computer Organization & Architecture

A Bitwise XNOR Calculator performs XNOR operation returns '1' if and only if both bits are the same, and '0' if they are different.

Bitwise XNOR Calculator

Boolean Algebra is a mathematical framework used in computer science for logical operations, including AND, OR, and NOT, to manipulate binary data.

Boolean Algebra

Calculates the broadcast address given an IP Address & CIDR.

Broadcast Address Calculator

networking

Cache memory is a high-speed data storage layer in a computer that stores frequently used information for quick access, improving processing speed.

Cache Memory

Calculate the cartesian product of two sets, which is the multiplication operation of Set A * Set B. This calculator can process both numbers and text!

Cartesian Product Calculator

discrete-math

The Central Limit Theorem states that the distribution of sample means approximates a normal distribution as the sample size becomes larger.

Central Limit Theorem

Statistics

Checksum is a method used in computing for error detection, ensuring data integrity by calculating a numerical value from a block of data.

Checksum

The Chinese Remainder Theorem is a theorem that gives a unique solution to a system of congruences with pairwise coprime moduli.

Chinese Remainder Theorem Calculator

Input your IP address/CIDR to calculate the netmask, usable ip range, network address, broadcast address, total # of host addresses, total # of available addresses, total # of subnets, and more..

IPv4 Subnetting

Circuits in digital logic are systems of interconnected components that manipulate binary information (0s and 1s) to perform computational tasks.

Circuits

Calculates the coefficient variation of a data set. Works for both sample and population.

Coefficient of Variation

Coloring assigns colors to graph vertices/edges under constraints, while chromatic number is the min. # of colors required to avoid adjacent colors.

Coloring and Chromatic Numbers

In discrete math, a combination is a way of selecting items from a larger set, where the order of the items does not matter.

Combinations Calculator

Combinations with repetitions refer to the number of ways to choose a subset of elements from a set where repetition is allowed.

Combinations with Repetitions

A composition of functions is a way of combining two or more functions to create a new function, where the output of one function becomes the input of another.

Composition of Functions

Conditional probability is the likelihood of an event occurring, given that another event has already occurred. It's a key concept in discrete math.

Conditional Probability

Covariance is a statistical measure that indicates the extent to which two variables change in tandem.

Covariance

CPU performance refers to the speed and efficiency at which a computer's central processing unit executes tasks, affecting overall system performance.

CPU Performance

Cyclic Redundancy Check (CRC) is a method used in computing to detect errors in data transmission by generating a check value from the data.

Cyclic Redundancy Check

Classifying Data in Statistics involves organizing and categorizing data into groups based on shared characteristics for easier analysis.

Classifying Data

Decimal conversions in computer organization refer to the process of converting decimal numbers into other number systems like binary, octal, or hexadecimal.

Decimal Conversions

Decimal Math in computer organization refers to calculations performed using base-10 number system, often used for financial and monetary computations.

Decimal Math Calculator

Calculates the default subnet mask based on an IP address.

Subnet Masks

A Diophantine equation is a polynomial equation where the solutions are required to be integers, often studied in number theory and algebra.

Linear Diophantine Equation Calculator

In discrete math, a direct proof is a method of proof that starts with given assumptions or premises and logically derives the conclusion.

Direct Proof

Directed graphs are a type of graph where edges have a direction, indicating a one-way relationship between nodes. 

Directed Graphs

Two sets are disjoint if their intersection is empty.

Disjoint Sets

The division algorithm states that given two integers a and b with b > 0, there exist unique integers q and r such that a = bq + r, 0 ≤ r < b.

Divisibility

An equivalence relation is a binary relation that is reflexive, symmetric, and transitive, which partitions a set into equivalence classes.

Equivalence Relation

An Euler circuit is a path that visits every edge of a graph exactly once, starting and ending at the same vertex.

Euler Circuits

An Euler path is a path that visits every edge of a graph exactly once, but may start and end at different vertices. It exists only in certain graphs.

Euler Paths

Excess notation is a method for representing signed integers in binary, where a bias is added to the actual number to eliminate negative values.

Excess Notation Converter

Algorithm for finding gcd and Bezout coefficients of two integers a and b by iteratively computing remainders using integer division.

Extended Euclidean Calculator

Learn how to calculate factorial values, understand its applications in combinatorics and probability, and find efficient algorithms for factorial computation.

Factorial Calculator

The Fibonacci Sequence is a series of numbers where each number is the sum of the two preceding ones, often starting with 0 and 1.

Fibonacci Sequence

Functions are mathematical objects that describe a relationship between inputs and outputs. 

Intro to Functions

Find the greatest common divisor of two numbers.

Greatest Common Divisor (GCD) Calculator

Generating functions are mathematical tools used to encode information about sequences of numbers into a single function, allowing for easier analysis.

Generating Functions

A geometric sequence multiplies the previous term by a fixed constant, the common ratio.

Geometric Sequence

A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number.

Geometric Series

Matching in graph theory is a set of edges that do not share any common vertices. It is used to model relationships between two sets of objects.

Matching

In graph theory, a walk is a sequence of vertices and edges that starts at one vertex and ends at another, following edges that connect them.

Walks

A Gray Code Converter is a tool in computer organization that translates binary numbers into Gray code, reducing errors in digital communications.

Gray Code Converter

Hamming Code is an error-detection and correction method in digital communication and data processing, enhancing data accuracy and reliability.

Hamming Code Calculator

Hamming Distance is a metric used in computer science to measure the difference between two binary strings. It's used for error detection and correction.

Hamming Distance Calculator

Harmonic Mean is a type of average, calculated by dividing the number of observations by the reciprocal of each number in the series.

Harmonic Mean

Hexadecimal conversions involve translating numbers between base 16 (hexadecimal) and other bases (like binary or decimal) in computer systems.

Hexadecimal Conversions

IEEE754 Floating Point Math is a standard for representing real numbers in computers, allowing for precise calculations in scientific computing.

IEEE754 Floating Point Math Calculator

Independent events in probability are those where the outcome of one event does not affect the outcome of another.

Independent Events

Indexed sets are collections of elements denoted by a specific index, often used to distinguish or order elements within a larger set.

Indexed Sets

Instruction Pipelining is a technique in computer architecture where multiple instructions are overlapped in execution to improve processing speed.

Instruction Pipelining

ISA is a blueprint that defines a computer's functionality, capabilities, and programming model, including its data types, instructions, and registers.

Instruction Set Architecture (ISA's)

Interrupts and Exceptions are signals sent to the processor to divert attention from the current process, allowing it to handle high-priority tasks.

Interrupts & Exceptions

"Introduction to Assembly" explores the low-level programming language used for direct hardware manipulation, crucial for system performance optimization.

Introduction to Assembly

Explore the basics of computer organization & architecture, including digital logic, data representation, and system design principles.

Intro to Computer Organization and Architecture

An introductory course exploring the basics of digital logic, including binary systems, logic gates, and how they influence computer organization.

Intro to Digital Logic

"Introduction to Memory" explores how computer memory functions, including data storage, retrieval, and the roles of different memory types.

Introduction to Memory

Intro to CPUs explores the central processing unit's role in computer organization, including data processing, instruction execution, and memory management.

Intro to CPUs

Propositional logic is a branch of logic that studies the relationships between propositions and their truth values using logical operators.

Propositional Logic

In discrete mathematics, relations are sets of ordered pairs that define a relationship between two or more sets, representing connections or links.

Intro to Relations

Intro to Statistics provides a foundational understanding of statistical concepts, including data analysis, probability, and statistical inference.

Introduction to Statistics

Inverse functions are functions that undo each other, meaning applying one function followed by the other gives the original input as the output.

Inverse Functions

Find the Modular Multiplicative Inverse of an Integer a and Modulo m. Primarily used in cryptography.

Modular Multiplicative Inverse (Inverse Modulo)

Calculate whether an IP Address falls under the Class A, B, C, D or E address ranges.

Classful Routing

IP Address to Binary Calculator

Convert IPv4 Address to Hexadecimal

Input your IPv6 address/Prefix to calculate the expanded IPv6 Address, total IPv6 addresses, total number of /64s, total number of subnets, the binary prefix, and the hexadecimal prefix.

IPv6 Subnetting

Calculates the interquartile range of a data set.

Interquartile Range

An irreflexive relation is one where no element is related to itself, i.e., (a, a) is not in the relation for all a.

Irreflexive Relation

The congruence relation a ≡ b (mod c) holds true if their difference is a multiple of c.

Congruence Modulo Calculator

Karnaugh Maps (K-Map) are graphical representations used in digital logic to simplify Boolean algebra expressions, aiding in circuit design.

Karnaugh Maps (K-Map)

Calculates the kurtosis of a data set. Works for both sample and population.

Kurtosis

Calculates the kurtosis excess of a data set. Works for both sample and population.

Kurtosis Excess

The smallest positive integer that is divisible by two or more integers. It can be found using prime factorization or the gcd of numbers.

Least Common Multiple

Logic Gates are fundamental building blocks of digital circuits that perform basic logical functions in computer organization.