Boolean Algebra (YouTube Video Index)


Boolean algebra, expression minimising, axioms, theorems, Karnaugh Maps and combinational logic circuit design
 F = A + 1 = 1 >> For this expression the result is one regardless as to the value of the Boolean variable A. This videos demonstrates why this is the case.
 F = A + 0 = A >> For this expression the result is always the value of the Boolean variable A. This videos demonstrates why this is the case.
 F = A And 0 = 0 >> For this expression the result is always 0 regardless as to the value of the Boolean variable A. This videos demonstrates why this is the case.
 F = A And 1 = A >> For this expression the result is always the value of the Boolean variable A. This videos demonstrates why this is the case.
 A Or Not(A) = 1 >> "Or'ing" a variable with its "Not'ed" version always gives one. This video shows why this is the case. The understanding of this axiom is key to understanding many theorems covered later in the playlists.
 F = Not(Not(A)) = A >> An important axiom that shows the effect of double "not'ing" a variable i.e. it keeps its value the same as shown in the video.
 F = A Or (A And B) >> Shows a useful 'short cut' for helping with the minimising of Boolean expressions.
 A Or (Not(A) And B) = A Or B >> Shows another useful 'short cut' for helping with the minimising of Boolean expressions.
 Associative Law (1 of 2) >> This video looks at an important Associative Law using truth tables and logic gates. Thus underpinning the law and giving further experience of using truth tables and logic circuits.
 Associative Law (2 of 2) >> This video looks at another important Associative Law using truth tables and logic gates. Thus underpinning the law and giving further experience of using truth tables and logic circuits.
 Commutative Laws >> This video uses truth tables to confirm the logic implied by the Commutative Laws. Thus underpinning the law and giving further experience of using truth tables.
 Distributive Law (1 of 5) >> This video illustrates an example of the Distributive law by reference to combinational logic circuits. Consequently it underpins the law whilst enhancing understanding of Boolean algebra and its relationship to combinational logic circuits.
 Distributive Law (2 of 5)>> Another example of a Distributive law is covered and this time it is considered using truth tables. This underpins the law whilst at the same time furthering the understanding of truth tables.
 Distributive Law (3 of 5) >> Again truth tables are used to illustrate another Distributive law.
 Distributive Law (4 of 5) >> Another Distributive law is considered and again truth tables are used in helping to under the law.
 Distributive Law (5 of 5) >> This last video in the sequence on the Distributive law again uses truth tables to enhance understanding of another distributive law.
 Introduction to Axioms >> An axiom is a fundamental rule that has to be taken for granted. This video introduces axioms and illustrates, by way of an example, a typical axiom.
 Axioms >> This video looks at other examples of axioms and at the end of the videos covers a very important axiom for use in the manipulation of Boolean expressions as will be shown in later video. PLEASE WATCH THE PREVIOUS VIDEO IN THIS PLAYLIST BEFORE YOU WATCH THIS VIDEO.
 Deriving a Theorem using axioms >> Axioms are use to derive theorems so that the theorems can be used to more efficiently assist with the minimising of Boolean expressions.
 Deriving a Theorem >> Another useful theorem is derived using axioms and then the theorem is used to show how Boolean expressions can be more efficiently minimised.
 Perfect Induction >> This video formalises the work done by the previous videos in the playlist. In particular it shows how a truth table can 'prove' that one Boolean expression does indeed equal another Boolean expression. This process of using truth tables in the way described in the video is called perfect induction.
 Two Variable Sum of Minterms >> This video demonstrates how to derive the sum of minterms from a two variable truth table. This is an important technique during the design of a combinational logic circuit.
 Three Variable Sum of Minterms >> This video demonstrates how to derive the sum of minterms from a three variable truth table. PLEASE WATCH THE PREVIOUS VIDEO FIRST
 Four Variable Sum of Minterms >> This video demonstrates how to derive the sum of minterms from a four variable truth table. YOU ARE ADVISED TO WATCH THE PREVIOUS TWO VIDEOS FIRST.
 Two Variable Karnaugh Map >> This video looks at a two variable Karnaugh Map and shows how it is possible to plot a sum of minterms onto the map. Appropriate techniques are then applied to the plot on the map to show how the sum of minterms can be minimised. AN ASSUMPTION IS MADE THAT YOU UNDERSTAND BOOLEAN VARIABLES AS INTRODUCED IN THE PREVIOUS VIDEOS.
 Karnaugh Map Examples (2 variables) >> Here this video builds on the work of the previous video by showing examples of minimising expressions using a two variable Karnaugh Map. It also introduces a plot that cannot be used to minimise an expression. PLEASE WATCH THE PREVIOUS VIDEO FIRST.
 Three Variable Karnaugh Map >> This video looks at a three variable Karnaugh Map and
shows how it is possible to plot a sum of minterms onto the map. Appropriate
techniques are then applied to the plot on the map to show how the sum of
minterms can be minimised.  Karnaugh Map Examples (Three Variables)>> Here this video builds on the work of the previous video by showing examples of minimising expressions using a three variable Karnaugh Map. It also introduces a plot that cannot be used to minimise an expression. PLEASE WATCH THE PREVIOUS VIDEO FIRST.
 Four Variable Karnaugh Map >> This video looks at a four variable Karnaugh Map and
shows how it is possible to plot a sum of minterms onto the map. Appropriate techniques are then applied to the plot on the map to show how the sum of minterms can be minimised.  Karnaugh Map Examples (4 variables) >> Here this video builds on the work of the previous video by showing examples of minimising expressions using a three variable Karnaugh
Map. It also introduces a plot that cannot be used to minimise an expression. PLEASE WATCH THE PREVIOUS VIDEO FIRST.  Combinational Logic Circuit Design >> Illustrates the steps involved in the design of a typical combinational logic circuit.
 Half Adder Design >> This video shows how to design a half adder using logic gates. IF YOU UNDERSTAND HOW TO DO THIS AS DEMONSTRATED IN THE VIDEO THEN YOU HAVE LEARNT MOST OF THE TECHNIQUES INTRODUCED IN THIS PLAYLIST.
 Half Subtractor >> Shows how to design a half subtractor
 De Morgan's Theorem >> This theorem is fundamental to logic and its application greatly assists in combinational logic circuit design.
 Universal Logic (Nand Gates) >> It is possible to implement any combinational logic circuit using one type of logic gate. Such gates are the Nand and Nor gate and they are referred to a universal gate. This video shows why a Nand gate is regarded as a universal gate.
 Half Adder Design (using universal gates) >> This video builds on the work of the last four videos and shows how a half adder can be built using just Nand gates. ENSURE YOU HAVE WATCHED THE PREVIOUS FOUR VIDEOS FIRST.
 Half Adder Design (using Nor gates) >> This video builds further on the work covered by the last five videos in the playlist and shows how a half adder can be built from just Nor gates.
 Exclusive Or Gate >> This video describes the XOR gate, its symbol, truth table and Boolean representation.
 Half Adder Design (XOR) >> This video revisits the design of a half adder and this time shows how an XOR gate can be used to help design the circuit.
 Logic Circuit Design for Memory >> Illustrates the steps involved in the design of a typical combinational logic circuit for the addressing of a computer's memory. This video is ideal to review most of the techniques that have been introduced earlier in this playlist.
 Combinational Logic Circuit Design (Memory) >> This video follows the same theme as the previous video and again shows how to design a combinational circuit using the techniques introduced in this playlist.
 Combinational Logic Circuit Design (Four Chips) >> This video follows the same theme as the previous two videos and again shows how to design a combinational circuit using the techniques introduced in this playlist.
 XOR gate >> This video answers a question on XOR gates from a YouTube subscriber