Logic Gate Expressions

This computer science video follows on from the video about combining logic gates. It covers how a logic gate diagram can be described with a Boolean expression. This includes how to come up with a valid expression for a given combination of logic gates and, conversely, how to draw a logic gate diagram for a given expression. The order of precedence of the logical operations NOT, AND and OR, and the importance of brackets, are also discussed. It was the British born mathematician George Boole who in the mid 19th century, long before digital computers were even dreamt of, first described complex logical arguments using algebraic expressions that could be manipulated and simplified. Almost 70 years later, the American mathematician and electrical engineer Claude Shannon, showed that ‘Boolean algebra’ could be applied to the design of switching circuits; circuits that effectively handled binary ones and zeros. It was the work of these men that laid the foundations for the invention of the modern digital computer, and this video will give you some insight into how their work came together. This video also sets the scene for learning the rules of Boolean algebra, a very powerful tool for computer circuit design.

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It's 2 different kinds of transistors inside that shunt the power in different directions.

[@duality4y]

you can build a Or with And and Not gates and vice versa And with Not and Or Gates. Which I find absolutely amazing.

[@ComputerScienceLessons]

What amazes me is that George Boole worked all of this out in the 19th century, based in the work of Aristotle from about 350 BC. :)KD

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[@ComputerScienceLessons]

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[@rezakamel1918]

thanks man for this video. there is 8 valid expressions in 06:20 not 4

[@ComputerScienceLessons]

Indeed :)KD

[@py_yogesh_1435]

It's a clear explanation thank u. Can u solve some boolean identity to draw the circuit😊

[@ComputerScienceLessons]

Thanks for the comment. If you're interested, I have made a sequence of videos on Boolean algebra. :) KD

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Thanx

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You're welcome :)KD

[@user-gx7yr6lc7c]

Sir, is it same as current syllabus? Btw I love how simplified you that much complex topic such a gem channel.

[@ComputerScienceLessons]

The fundamental concepts have not changed since the 1950's. Some people use different symbols for the logical operations. I have used ^ for AND, v for NOT and ¬ for NOT because you can find them all on a keyboard. The fundamental concepts are universal, regardless of the syllabus you follow :)KD

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[@wildjimmy7]

Please correct me if I'm wrong, but the logic circuit you drew from the Boolean expression Z=(A and B) and NOT B is incorrect. If B is high than the circuit will not have an output due to the NOT gate feeding the second AND gate. If B is low than the first gate will not have an output, which will cause the second gate to again have no output. B can not be high and low at the same time in an AND gate configuration.

[@ComputerScienceLessons]

Hi James. The logic gate diagram does indeed match the expression (the object of the exercise), but as you have quite correctly pointed out, the circuit is pretty much useless. Examination of the truth table reveals that the value of Z is always 0, which means the whole thing could replaced with a single wire carrying no voltage at all. A B NOT B Z 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 If you are interested, my videos on Karnaugh maps and Boolean algebra cover techniques for simplifying expressions and therefore the circuits they represent.

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Thanks :)KD

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Thnku

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Can you please explain how to prove laws using algebraic method?

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Jim Pytel.

[@giuliadiriso5205]

Ist it also right if i would write b and (not a) instead of (not a) and b

[@ComputerScienceLessons]

Yes it is. This is known as the commutative law of Boolean algebra. However, not(a and b) is something different. Furthermore not(b and a) is the same as not(a and b) :)KD

[@alaintristanlado4001]

what would be the input if 2 end gate connected together to not gate?

[@ComputerScienceLessons]

Not sure what you mean?