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Hello and welcome to the first[br]video on Boolean logic.

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And Boolean expressions. You[br]might know this topic in an

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alternative name because the[br]same topic sometimes also

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referred to as digital Logic or[br]Boolean algebra or algebra of

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proposition. What this topic is[br]looking at is looking at a

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collection of input values.

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A collection of operators.

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That sometimes we refer to as[br]logic gates and looking at what

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happens at the end, what is a[br]particular set of of these

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inputs and operators? What kind[br]of outputs you can end up with?

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Now the origonal part of this[br]coming from the at the very very

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beginning, the computer has been[br]built up from logic circuits.

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Tiny, tiny little circuits and[br]then depending on which circuits

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you connected together, you were[br]able to tie the computer to do

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different things so.

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The input and output values can[br]be recorded in a number of

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different ways. Again, there are[br]two common ways.

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One is the true for set up and[br]the other one is the 1 zero set

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up again. It comes from the fact[br]that logic circuits can be

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turned on or off true and one is[br]equal to the on position and

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force in OR equal to the off[br]position. Remember circuits turn

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it on or turn it off. So let's

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look at. What are the[br]basic Boolean operations? The

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first Boolean operation?

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Is the end operation now this[br]end operation sometimes just

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written out as end in capital[br]letters sometimes is referred to

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as this symbol?

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And sometimes it's referred to[br]as a multiplication simple

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symbol because it works like[br]ordinary multiplication within

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the binary system. Now it also[br]has got in digital logic. If

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you're looking at the circuits[br]themselves. If you're looking

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at how to build boards[br]together, it has got a logic

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gate symbol and that logic[br]gate symbol is this one.

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Now this tells you that this[br]endgate can take a minimum

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of two input values and it[br]will give you always one

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output value.

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So what does the end gate do[br]now? The end gate is actually

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working as if you had a water[br]pipe fixed with two taps on it,

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one after the other.

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So when we have water flow[br]through, the water will flow

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through only if both of the[br]tabs are open. If I turn

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this tab off.

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The voter will stop here if I[br]turn this step on when I leave

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this tab of the water will stop[br]here, so water still doesn't

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flow through an. Obviously, if[br]I have both taps turned off,

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the water doesn't go further[br]than here. So what are we only

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go through if all of these[br]steps are on, so would have can

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go through only this way. Now[br]how can we sort of summarize

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this information in a nice and[br]simple visual format? That's

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why truth tables.

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Has been invented through.[br]Tables are simple tables which

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tells you what are the input[br]values or other possible input

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values that can come. What is[br]the logic gate or what is the

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Boolean operation that we use[br]here and then? What will be the

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end result of that Boolean[br]operation for every possible

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income combinations? Now let's[br]look at the simple examples.

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Let's see how does the P&Q

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operation works. B is an input[br]queue, is a different input.

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What happens if I combine them[br]together? What will be the

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common output so P.

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And Q.

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And here will be my output.

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Now what kind of setups can the[br]two taps have? While I can turn

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both of them on?

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I can turn one of them on[br]the other one off, all in

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the other combination.

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Or I can have both[br]of them turned off.

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So what did we say? The water[br]can only go through if both of

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the taps are on?

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Every other combination will[br]stop the water from flowing, so

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this is the truth table[br]accompanying the end.

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Operation. With this Boolean[br]trip tables, you need to know

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them. You need to understand[br]them because later on we'll be

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combining more than just one[br]single operation together and

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see what happens if we start to[br]mix them up. So this was the

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first one, the end operation.[br]Let's have a look at the next

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one, which is the OR operator.[br]Now the symbol for the OR

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operator can be this small away.[br]The opposite, the turned upside

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of the end or the addition[br]because it works.

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Like the audition.

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And if you are coming from[br]the engineering background.

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You can see either this.

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Symbol or this symbol?

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For the OR gates, again it[br]takes in at least two

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incoming values and gives you[br]one outgoing value, so at

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least two inputs, one output.

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You can think about the OR gate.

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As water pipes but fixed

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now. In a different way now[br]these water pipes I fixed

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together in a parallel[br]fashion and on each branch

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we have got a tap.

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So what happens in this case?[br]Now if I turn this tap off, stop

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the water flowing here, but I[br]don't turn this stuff off.

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The water will be able to bypass[br]that turned side and fluid flow

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through. Here the same the other[br]way around. And obviously if

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both of the tabs are open then[br]the voter have got the choice of

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flowing through one or the[br]other, so the OR operation.

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Opposite to what the end does,[br]it only stops the water. In one

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case it stops the water if both[br]of the taps are turned off.

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So what does it look like in the[br]truth table fashion? So again.

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P or Q. What are the possible[br]income combinations and what are

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the possible outcome[br]combinations of these? So again,

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I can have two values.

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Two input values P.

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K.

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So again, what are the different[br]input combinations for these two

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values? The P&QA quick trick.

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True, true Force Force 3434.[br]This fact comes from I've

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got two input values.

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P or K, but all both of them can[br]be true or false, so I only have

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got two possible switch stands.[br]So 2 to the power of two gives

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me 4, but two is the number of[br]input values and two is the

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number of possible outcomes like[br]trues or force.

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So what did we establish if[br]both of the taps are turned

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on, then the voter can flow[br]through. If one of the taps

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are turned on, then the water[br]can flow through that branch

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and bypass the off tab.

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But if both of the taps are[br]turned off than the water it

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stopped. So that's when this[br]this operation is forced.

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So the next operation that I[br]would like to talk about is the

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not operation, which sometimes[br]also used this symbol.

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Sometimes this symbol and[br]sometimes it used just by a bar

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over the input for the pictorial[br]symbol for the Northgate. For

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engineers is this it's a little[br]triangle with a little circle at

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the end now.

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Compared with the others, the[br]not operation only have one

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input and has one output.

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OK, so that state to wait as you[br]something. So if I have got just

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one input then that input P.

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Can only be true or false and[br]then not P.

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But what is not true? What[br]is not true is force and

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what is not force is true.[br]So the not operation has

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got a very special role. It[br]flips it inverts it changes

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the input to its opposite.

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The next simple operation[br]is the X or.

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Which has got this symbol, so it[br]doesn't have that many symbol as

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the not. So that's easier. And[br]the exors pictorial symbol for

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joining as circuit.

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Is the OR gate?

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But with an extra leg added to[br]it so it can take again at least

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two inputs. Or if we use the[br]alternative way of the X or.

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And it would look.

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Something like that.

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OK, now this is called the[br]axle operation because it's

0:10:20.010,0:10:20.550
exclusive.

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Or

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so it's exclusively one or the[br]other input, so the xclusive

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or the X or operation filters[br]out the input values when the

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inputs are the same. So what[br]do I mean by that? If I have

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got inputs P&Q?

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What will the acts or do[br]to them?

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So again, be can be true[br]to force force and Q is

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true force three force.

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So exclusive, or if the inputs[br]are the same, which is this

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case? Because both of them are[br]true. The Exor Gate gives you a

0:11:09.425,0:11:13.215
4th signal. Basically the axle[br]gates stops the signal going

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through. If one is to the other[br]one is forced then that's when

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the signal can go through and[br]again because force enforces the

0:11:22.311,0:11:26.480
same input value that the EXOR[br]gate stops your signal going

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through. And remember that I[br]mentioned at the beginning of

0:11:30.270,0:11:34.584
this video. These are based on[br]the electric circuits and then

0:11:34.584,0:11:38.500
you wanted to manipulate at the[br]very, very early stages or

0:11:38.500,0:11:42.060
lippit stages of computing you[br]wanted to manipulate where the

0:11:42.060,0:11:45.264
electrical signal goes doesn't[br]go through here doesn't go

0:11:45.264,0:11:48.468
through that you wanted to[br]manipulate and filter out

0:11:48.468,0:11:52.384
certain inputs in favor of other[br]inputs. So these different gates

0:11:52.384,0:11:56.656
give you that kind of option of[br]turning them around. Saying, I

0:11:56.656,0:12:00.572
don't want this input, I want[br]that that input combination to

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go through and nothing else.

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There are a couple of more[br]operations that I would like

0:12:06.720,0:12:09.330
to talk about. These are[br]slightly more complicated. I

0:12:09.330,0:12:12.810
can't really give you any nice[br]and simple example of why they

0:12:12.810,0:12:16.580
work in here. We just have to[br]learn that this is the way

0:12:16.580,0:12:19.770
that they work, so one of them[br]is that you've done.

0:12:22.050,0:12:25.047
And the symbol for that[br]is this forward error.

0:12:26.440,0:12:30.350
So again. I've got inputs P&Q.

0:12:31.320,0:12:35.220
And then what will be[br]the Alpha output of the

0:12:35.220,0:12:37.170
P IF then Q operation?

0:12:39.620,0:12:46.586
So true true Force force[br]three force, three force.

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Sometimes this also[br]called the implies.

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So true implies true, that is

0:12:57.196,0:13:04.340
true. But true cannot imply[br]force, so this one is force

0:13:04.340,0:13:06.592
force can imply true.

0:13:08.150,0:13:11.290
And force can imply force[br]that's true. Again, this is

0:13:11.290,0:13:14.430
probably going to be the most[br]difficult gate to understand

0:13:14.430,0:13:18.198
why this works. You just have[br]to learn the truth tables, and

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once you know the truth[br]tables, you can apply it to

0:13:21.652,0:13:22.908
any kind of combinations.

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And the last operation that I[br]would like to talk about is that

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if and only if.

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And the symbol for that is[br]an arrow that goes both

0:13:36.903,0:13:40.676
ways. So if I have got the[br]two inputs again P&Q.

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The P if and only Q[br]will work this way.

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33443434.

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This one is only true.

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If both inputs are the same, so[br]true and true are the same, so

0:14:05.488,0:14:09.470
this will be true. True annefors[br]are different, so the output

0:14:09.470,0:14:14.538
will be force same for the third[br]right and for some for side the

0:14:14.538,0:14:19.968
same. So this is true in here.[br]Now if you look at this one and

0:14:19.968,0:14:24.312
if you remember the X or you can[br]support that these two

0:14:24.312,0:14:29.018
operations if and only if an the[br]X or are doing exactly the

0:14:29.018,0:14:30.828
opposite in this using this.

0:14:30.880,0:14:37.312
Operation I can filter out the[br]same input values and stop the

0:14:37.312,0:14:38.920
different input values.

0:14:40.000,0:14:43.132
So that's again a very useful[br]operation to have.

0:14:46.120,0:14:50.748
This short video was intended to[br]expose you to the basics of the

0:14:50.748,0:14:54.664
Boolean logic or digital logic[br]and show you had the truth.

0:14:54.664,0:14:58.936
Tables can be built up and what[br]are the most commonly used

0:14:58.936,0:15:03.208
operations to be able to follow[br]up on digital logic? You will

0:15:03.208,0:15:07.836
need to be able to know this by[br]heart, so these are different

0:15:07.836,0:15:12.108
operations that every time you[br]need to apply them you will be

0:15:12.108,0:15:15.668
have to be very, very confident[br]knowing these operations how

0:15:15.668,0:15:19.176
they work. What they do? What[br]kind of inputs they let

0:15:19.176,0:15:22.520
through an? What kind? What[br]kind of inputs they stop from

0:15:22.520,0:15:25.560
going through? And again, as I[br]mentioned at the beginning,

0:15:25.560,0:15:28.600
this is all coming from the[br]basic principles that went

0:15:28.600,0:15:31.640
first. Human started team when[br]the computers they build them

0:15:31.640,0:15:33.464
together from very tiny basic[br]circuits.