Number Bases, Decimal, Binary, Hexadecimal, Octal - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to represent numbers in different bases, including decimal, binary, hexadecimal and octal.
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Convert Integer to Binary, Euclidean Division Theorem - Discrete Mathematics
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This Discrete Mathematics video explains how to convert an integer to binary.
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Convert Integer to Octal, Euclidean Division Theorem - Discrete Mathematics
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This Discrete Mathematics video explains how to convert an integer to octal.
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Convert Integer to Hexadecimal, Euclidean Division Theorem - Discrete Mathematics
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This Discrete Mathematics video explains how to convert an integer to hexadecimal.
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Convert Non-Integer to Binary, Repeating Digits - Discrete Mathematics
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This Discrete Mathematics video explains how to convert a non-integer to binary.
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Convert Non-Integer to Binary - Discrete Mathematics
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This Discrete Mathematics video explains how to convert a non-integer to binary.
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Convert Non-Integer to Hexadecimal - Discrete Mathematics
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This Discrete Mathematics video explains how to convert a non-integer to hexadecimal.
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Convert Hexadecimal to Binary and Octal - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to convert between hexadecimal, binary and octal number bases.
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Adding Binary Numbers - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to add binary numbers.
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Adding Hexadecimal Numbers - Discrete Mathematics
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This Discrete Mathematics video explains how to add hexadecimal numbers.
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Subtracting Binary Numbers - Discrete Mathematics
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This Discrete Mathematics video explains how to subtract binary numbers.
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Subtracting Hexadecimal Numbers - Discrete Mathematics
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This Discrete Mathematics video explains how to subtract hexadecimal numbers.
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Multiplying Binary Numbers - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to multiply binary numbers.
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Multiplying Hexadecimal Numbers - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to multiply hexadecimal numbers.
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Dividing Binary Numbers - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to divide binary numbers.
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Dividing Hexadecimal Numbers - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to divide hexadecimal numbers.
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Ten's Complement, Subtraction - Discrete Mathematics
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This Discrete Mathematics video explains how to subtract integers using complements.
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Two's Complement, Binary Subtraction - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to subtract integers using complements.
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Two's Complement, Represent Negative Binary Numbers - Discrete Mathematics
DrOfEng
This Discrete Mathematics explains how negative numbers are represented in computer memory using the two's complement.
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Normalised Scientific Notation - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how real numbers can be represented using normalised scientific notation, which is useful for understanding how real numbers are stored in computer memory.
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Real Numbers, IEEE754 Floating Point Standard - Discrete Mathematics
DrOfEng
This Discrete Mathematics explains how real numbers are stored in computer memory using the IEEE754 floating point standard.
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Real Numbers, IEEE754 Floating Point Standard, Example - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on converting a binary number to a float using the IEEE754 floating point standard.
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Algorithms, Pseudocode - Discrete Mathematics
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This Discrete Mathematics video provides an introduction to mathematical algorithms and pseudocode.
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Horner's Method, Evaluating Polynomials - Discrete Mathematics
DrOfEng
This Discrete Mathematics video describes Horner's method for evaluating polynomials using a worked example. The pseudocode is provided to show how you would implement the algorithm in a computer.
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Collision Detection, Games, Computer Graphics - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on how write a collision detection algorithm, which is used in computer graphics and games.
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Encryption Algorithm, Cryptography, Caesar Cipher - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on how to write a cryptographic algorithm. Basic modular arithmetic is also covered.
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Lottery Algorithm, Binomial Theorem - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how the number of combinations in the lottery can be determined using the binomial theorem, which is also verified using a computer program.
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Sigma Notation, Iteration and Recursion - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains sigma (or summation) notation using several examples.
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Geometric Series, Iteration and Recursion - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains the geometric series and derives a closed form relation for this series.
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Arithmetic Series, Iteration and Recursion - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains the arithmetic series and derives a closed form relation for this series.
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Fibonacci Sequence, Iteration - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains Iteration using the well-known Fibonacci sequence.
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Recursion, Fibonacci Sequence - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains recursion using the well-known Fibonacci sequence.
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Recursion, Factorial, Recurrence Relation - Discrete Mathematics
DrOfEng
This Discrete Mathematics video derives the recurrence relation of a factorial sequence using a worked example.
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Recurrence Relations, Standard Form, Properties - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains the standard linear form of recurrence relations and their properties, including linear, homogeneous, order and variable coefficients.
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Recurrence Relations, 1st Order, Homogeneous, Solution - Discrete Mathematics
DrOfEng
This Discrete Mathematics video derives the general solution for a 1st order homogeneous recurrence relation with constant coefficients.
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Recurrence Relations, 2nd Order, Homogeneous, Solution - Discrete Mathematics
DrOfEng
This Discrete Mathematics video derives the general solution for 2nd order homogeneous recurrence relations with constant coefficients.
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Fibonacci Recurrence Relation, Solution, Example - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on the solution to the Fibonacci recurrence relation.
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Recurrence Relation, 2nd Order, Solution, Example - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on the solution to a recurrence relation with one repeated real root.
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Non-Homogeneous 2nd Order Recurrence Relations, General Solution - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains the method of superposition for determining the general solution for 2nd order non-homogeneous recurrence relations.
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Non-Homogeneous 2nd Order Recurrence Relations, Solution, Special Cases - Discrete Mathematics
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This Discrete Mathematics video identifies two special cases that need to be considered when selecting a particular solution to a non-homogeneous 2nd order recurrence relation.
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2nd Order Non-Homogeneous Recurrence Relations, Example - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on 2nd order non-homogeneous recurrence relations.
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2nd Order Non-Homogeneous Recurrence Relations, Example - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on 2nd order non-homogeneous recurrence relations.
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Computational Complexity, Introduction - Discrete Mathematics
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This Discrete Mathematics video provides an introduction to computational complexity.
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Big O, Informal Definition - Discrete Mathematics
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This Discrete Mathematics video provides an informal definition of Big O.
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Comparing Growth Rates, Logarithms - Discrete Mathematics
DrOfEng
This Discrete Mathematics video compares the growth rates of logarithms to other functions and describes the basic properties of logarithms.
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Typical Growth Rates, log(N), N, Nlog(N), N^2, 2^N, N! - Discrete Mathematics
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This Discrete Mathematics video covers the typical growth rates encountered when determining the complexity of algorithms.
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Big O, O(f(N)), Formal Definition - Discrete Mathematics
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This Discrete Mathematics video explains the formal definition of Big O using a worked example.
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Big O, O(f(N)), Formal Definition, Examples - Discrete Mathematics
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This Discrete Mathematics video covers worked examples on the formal definition of Big O.
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Big O, Lazy C Approach, Example - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on Big O.
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Triangle Inequality, Refine Big O Calculations - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how the triangle inequality can be used to determine the order of a function using a worked example.
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Big O Inequality, Different Constants c and n0 - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to predict the order of a function using Big O and better constants, drawing an analogy to predicting the growth of algorithms.
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Big O, Refined Calculation, Large N - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains a Big O calculation that is more refined for algorithms i.e. positive function and large N.
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Big O, Refined Calculation, Example - Discrete Mathematics
DrOfEng
This Discrete Mathematics video covers a worked example on the refined Big O calculation.
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Bubble Sort, Big O, O(N^2), Analysis of Algorithms - Discrete Mathematics
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This Discrete Mathematics video explains how to determine the order of the Bubble Sort algorithm.
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Bubble Sort, Big O, O(N^2), Recurrence Relation - Discrete Mathematics
DrOfEng
This Discrete Mathematics video explains how to determine the order of the Bubble Sort algorithm by deriving the recurrence relation.
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Merge Sort, Algorithm Analysis, Big O, O(nlogn) - Discrete Mathematics
DrOfEng
This Discrete Mathematics video derives the Big O of the Merge Sort algorithm.
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Binary Search Algorithm, Analysis, Big O, O(logn) - Discrete Mathematics
DrOfEng
This Discrete Mathematics video derives the Big O of the Binary Search algorithm.
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Binary Search, Analysis, Big O, O(logn), Recurrence Relation - Discrete Mathematics
DrOfEng
This Discrete Mathematics video derives the Big O of the Binary Search algorithm using recurrence relations.
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Multiplication Rule for Counting - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the multiplication rule for counting.
Multiplication Rule for Counting, Examples - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the multiplication rule for counting with worked examples to reinforce your understanding.
Addition Rule for Counting - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the addition rule for counting, which is used to determine the number outcomes for mutually exclusive tasks.
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Addition and Multiplication Rules for Counting, Example - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the multiplication (product) and addition (sum) rules for counting. A worked example is covered to reinforce your understanding.
Inclusion-Exclusion Principle - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the inclusion-exclusion principle.
Inclusion Exclusion Principle, Example - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the inclusion-exclusion principle. A worked example is covered to reinforce your understanding.
Permutations - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on permutations which is the number of rearrangements of the elements of a set. The permutations of a set with n elements are defined by n! (n factorial).
r-permutation - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on r-permutation, which is an ordered arrangement of r distinct objects r chosen from a a set of n objects and denoted by P(n,r).
r-permutation, Examples - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on r-permutation, which is an ordered arrangement of r distinct objects r chosen from a a set of n objects and denoted by P(n,r). Worked examples are covered to reinforce your understanding.
Permutations Vs Combinations - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial that explains the difference between r-permutations and r-combinations. Order matters in permutations but order does not matter in combinations.
Combinations, Examples - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on r-combinations. Worked examples are covered to enhance your understanding.
0:00 Example on r-combinations and the multiplication rule
3:01 Example on r-combinations applied to the lottery
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Combinations, Multiple Categories - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on combinations in multiple categories.
Combinations, Multiple Categories, Examples - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on combinations in multiple categories. Worked examples are covered for practice.
Binomial Theorem - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the binomial theorem. The binomial coefficients are determined using the combination formula or Pascal's triangle.
Lexicographic Ordering - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on lexicographic ordering. Lexicographic ordering is one of the applications of permutations and combinations.
0:00 Definition of lexicographic ordering
2:43 Lexicographic ordering algorithm with worked examples
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Cartesian Product of Sets - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the Cartesian product of sets.
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Functions - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on functions.
Binary Operations - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on binary operations.
Boolean Algebra, Truth Tables, Axioms - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on boolean algebra and truth tables.
Boolean Algebra, Power of a Set, Example - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on verifying if the power of a set is a boolean algebra.
Boolean Algebra, Switching Circuits, Example - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial with a worked example on applying boolean algebra to switching circuits.
de Morgan's Laws, Dual Boolean Expressions - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on de Morgan's laws and the duals of boolean expressions.
Equivalence of Boolean Expressions - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the equivalence of boolean expressions.
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Voting Machine, Boolean Algebra, Example - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the voting machine, which is a problem on designing a voting circuit using boolean algebra.
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Minterm, Disjunctive Normal Form - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on the minterm and disjunctive normal form in a set.
Karnaugh Maps, K-Map - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on using Karnaugh maps to simplify boolean expressions.
Karnaugh Maps, K-Map, Example - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on using Karnaugh maps to represent a boolean expression using a worked example.
Karnaugh Map Algorithm, Minimal Boolean Expression - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on a Karnaugh map algorithm for obtaining the minimal representation of a boolean expression.
Don't Care Karnaugh Maps - Discrete Mathematics
DrOfEng
This discrete mathematics video covers a tutorial on don't care Karnaugh maps algorithm for obtaining the minimal representation of a boolean expression where some of the inputs may be invalid.
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Logic Statements, Symbols - Discrete Mathematics
DrOfEng
This video explains logic, including logic statements, symbols, truth tables and connectives, which will be used to construct the main types of logic gates for circuits.
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Logic Circuits, Logic Gates - Discrete Mathematics
DrOfEng
This video explains logic circuits, including worked examples, diagrams, symbols, truth tables and boolean expressions.
0:00 Logic gates and circuits
1:41 Worked examples
How a Breadboard Works, Logic Gates, Basic Electronics - Discrete Mathematics
DrOfEng
This explains how a breadboard electronics work using a simulation to show the wires, circuit diagram, connections and power supply. You will understand what a breadboard is used for.
Build your own electrical circuits here: https://www.tinkercad.com/
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NOT Gate, Logic Circuits, Digital Electronics - Discrete Mathematics
DrOfEng
This video explains the not gate (one of the 7 logic gates), including the logic circuit diagram, symbol, truth table, and ic. The point of a not gate is that it is an inverter, which inverts the input voltage from high to low and vice versa.
How a breadboard works https://youtu.be/8vFdPteTtdU
Build your own electrical circuits here: https://www.tinkercad.com/
Datasheet for 74HC04 Hex Inverter https://www.alldatasheet.com/datasheet-pdf/download/15523/PHILIPS/74HC04.html
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AND Gate, Logic Circuits, Boolean Algebra - Discrete Mathematics
DrOfEng
This video explains the and gate (one of the 7 logic gates), including truth table, symbol, logic circuit, ic, rule and formula.
How a breadboard works https://youtu.be/8vFdPteTtdU
Building a logic circuit with a NOT gate https://youtu.be/xuoGTWr2_lM
Build your own electrical circuits here: https://www.tinkercad.com/
Datasheet for 74HC08 AND gate https://www.alldatasheet.com/datasheet-pdf/pdf/15524/PHILIPS/74HC08.html
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comments
XOR Gate, Logic Circuit Diagram, Truth Table, Digital Electronics - Discrete Mathematics
DrOfEng
This video explains how to construct an xor gate using the truth table and logic circuit diagram, what it does, how it works, the IC numbers and symbol.
How a breadboard works https://youtu.be/8vFdPteTtdU
Building a logic circuit with a NOT gate https://youtu.be/xuoGTWr2_lM
Building a logic circuit with an AND gate https://youtu.be/2szTmHspb-I
Build your own electrical circuits here: https://www.tinkercad.com/
Half Adder, Logic Circuit, Karnaugh Map, Truth Table, Digital Electronics - Discrete Mathematics
DrOfEng
This video explains what is a half adder with the logic diagram and truth table, the problem with it and the difference between a full adder, the equation for it, and what chip is used in the circuit.
How a breadboard works https://youtu.be/8vFdPteTtdU
Building a logic circuit with a NOT gate https://youtu.be/xuoGTWr2_lM
Build your own electrical circuits here: https://www.tinkercad.com/
2
comments
Full Adder, Logic Circuit Diagram, Truth Table, Digital Electronics - Discrete Mathematics
DrOfEng
The video explains what a full adder is vs a half adder and the difference between them, how the circuit is built from or using half adders. This gives the foundation to understanding what does an 8 bit full adder do and whether a 2 bit adder is a full adder.
How a breadboard works https://youtu.be/8vFdPteTtdU
Building a logic circuit with a NOT gate https://youtu.be/xuoGTWr2_lM
Building a half adder https://youtu.be/6v-_Id_oyjw
Build your own electrical circuits here: https://www.tinkercad.com/
2-Bit Adder, Logic Circuits, Digital Electronics - Discrete Mathematics
DrOfEng
How to make a 2 bit binary number adder circuit by connecting two full adders. The truth table and circuit diagram show what a bit adder does and if it is the same as a half adder.
How a breadboard works https://youtu.be/8vFdPteTtdU
Building a logic circuit with a NOT gate https://youtu.be/xuoGTWr2_lM
Building a full adder https://youtu.be/eBOFQNifcOE
Build your own electrical circuits here: https://www.tinkercad.com/
4-Bit Ripple Carry Adder, Logic Circuit - Discrete Mathematics
DrOfEng
The video explains how to build a 4-bit adder circuit, what it does and how it works. It uses the same 4 full adders to do 4-bit addition, which is the major drawback as the carry out has to be rippled through each full adder.
Two's Complement, Binary Numbers, Logic Circuit - Discrete Mathematics
DrOfEng
What is the two's (2's) complement. You learn the trick to calculate it for any number such as binary, positive and negative (e.g. of 1010, 43, 00000000, -17, 11111) using the one's (1's) complement. An example of a logic circuit design using a 4-bit full adder to show how the 2's complement is determined by a computer.
How a breadboard works https://youtu.be/8vFdPteTtdU
Building a logic circuit with a NOT gate https://youtu.be/xuoGTWr2_lM
Building a 4-bit adder https://youtu.be/_S7-zS_rUhQ
Build your own electrical circuits here: https://www.tinkercad.com/
1
comment
4-bit Full Subtractor Circuit, IC 7483, Truth Table - Discrete Mathematics
DrOfEng
How to build a circuit using a 7483 IC and truth table for a 4-bit binary subtractor using adder and inverter, and what it is.
How a breadboard works https://youtu.be/8vFdPteTtdU
Building a logic circuit with a NOT gate https://youtu.be/xuoGTWr2_lM
Building a 2's complement logic circuit https://youtu.be/wxCY9RoM_1g
Build your own electrical circuits here: https://www.tinkercad.com/
Adding Binary Numbers - Discrete Mathematics
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