[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:18.79,0:00:22.95,Default,,0000,0000,0000,,Hello and welcome to the first\Nvideo on Boolean logic.
Dialogue: 0,0:00:23.62,0:00:27.85,Default,,0000,0000,0000,,And Boolean expressions. You\Nmight know this topic in an
Dialogue: 0,0:00:27.85,0:00:31.23,Default,,0000,0000,0000,,alternative name because the\Nsame topic sometimes also
Dialogue: 0,0:00:31.23,0:00:35.89,Default,,0000,0000,0000,,referred to as digital Logic or\NBoolean algebra or algebra of
Dialogue: 0,0:00:35.89,0:00:40.54,Default,,0000,0000,0000,,proposition. What this topic is\Nlooking at is looking at a
Dialogue: 0,0:00:40.54,0:00:42.23,Default,,0000,0000,0000,,collection of input values.
Dialogue: 0,0:00:42.83,0:00:44.93,Default,,0000,0000,0000,,A collection of operators.
Dialogue: 0,0:00:45.52,0:00:49.84,Default,,0000,0000,0000,,That sometimes we refer to as\Nlogic gates and looking at what
Dialogue: 0,0:00:49.84,0:00:54.16,Default,,0000,0000,0000,,happens at the end, what is a\Nparticular set of of these
Dialogue: 0,0:00:54.16,0:00:58.48,Default,,0000,0000,0000,,inputs and operators? What kind\Nof outputs you can end up with?
Dialogue: 0,0:00:58.48,0:01:03.16,Default,,0000,0000,0000,,Now the origonal part of this\Ncoming from the at the very very
Dialogue: 0,0:01:03.16,0:01:06.76,Default,,0000,0000,0000,,beginning, the computer has been\Nbuilt up from logic circuits.
Dialogue: 0,0:01:06.76,0:01:10.36,Default,,0000,0000,0000,,Tiny, tiny little circuits and\Nthen depending on which circuits
Dialogue: 0,0:01:10.36,0:01:14.68,Default,,0000,0000,0000,,you connected together, you were\Nable to tie the computer to do
Dialogue: 0,0:01:14.68,0:01:15.76,Default,,0000,0000,0000,,different things so.
Dialogue: 0,0:01:15.91,0:01:20.91,Default,,0000,0000,0000,,The input and output values can\Nbe recorded in a number of
Dialogue: 0,0:01:20.91,0:01:24.25,Default,,0000,0000,0000,,different ways. Again, there are\Ntwo common ways.
Dialogue: 0,0:01:24.89,0:01:30.95,Default,,0000,0000,0000,,One is the true for set up and\Nthe other one is the 1 zero set
Dialogue: 0,0:01:30.95,0:01:35.50,Default,,0000,0000,0000,,up again. It comes from the fact\Nthat logic circuits can be
Dialogue: 0,0:01:35.50,0:01:40.81,Default,,0000,0000,0000,,turned on or off true and one is\Nequal to the on position and
Dialogue: 0,0:01:40.81,0:01:44.98,Default,,0000,0000,0000,,force in OR equal to the off\Nposition. Remember circuits turn
Dialogue: 0,0:01:44.98,0:01:48.01,Default,,0000,0000,0000,,it on or turn it off. So let's
Dialogue: 0,0:01:48.01,0:01:53.93,Default,,0000,0000,0000,,look at. What are the\Nbasic Boolean operations? The
Dialogue: 0,0:01:53.93,0:01:55.75,Default,,0000,0000,0000,,first Boolean operation?
Dialogue: 0,0:01:57.10,0:02:02.01,Default,,0000,0000,0000,,Is the end operation now this\Nend operation sometimes just
Dialogue: 0,0:02:02.01,0:02:07.41,Default,,0000,0000,0000,,written out as end in capital\Nletters sometimes is referred to
Dialogue: 0,0:02:07.41,0:02:08.88,Default,,0000,0000,0000,,as this symbol?
Dialogue: 0,0:02:09.65,0:02:12.78,Default,,0000,0000,0000,,And sometimes it's referred to\Nas a multiplication simple
Dialogue: 0,0:02:12.78,0:02:15.57,Default,,0000,0000,0000,,symbol because it works like\Nordinary multiplication within
Dialogue: 0,0:02:15.57,0:02:19.74,Default,,0000,0000,0000,,the binary system. Now it also\Nhas got in digital logic. If
Dialogue: 0,0:02:19.74,0:02:22.87,Default,,0000,0000,0000,,you're looking at the circuits\Nthemselves. If you're looking
Dialogue: 0,0:02:22.87,0:02:26.70,Default,,0000,0000,0000,,at how to build boards\Ntogether, it has got a logic
Dialogue: 0,0:02:26.70,0:02:30.18,Default,,0000,0000,0000,,gate symbol and that logic\Ngate symbol is this one.
Dialogue: 0,0:02:32.49,0:02:36.74,Default,,0000,0000,0000,,Now this tells you that this\Nendgate can take a minimum
Dialogue: 0,0:02:36.74,0:02:40.98,Default,,0000,0000,0000,,of two input values and it\Nwill give you always one
Dialogue: 0,0:02:40.98,0:02:41.75,Default,,0000,0000,0000,,output value.
Dialogue: 0,0:02:43.77,0:02:48.28,Default,,0000,0000,0000,,So what does the end gate do\Nnow? The end gate is actually
Dialogue: 0,0:02:48.28,0:02:53.14,Default,,0000,0000,0000,,working as if you had a water\Npipe fixed with two taps on it,
Dialogue: 0,0:02:53.14,0:02:54.53,Default,,0000,0000,0000,,one after the other.
Dialogue: 0,0:02:57.61,0:03:01.97,Default,,0000,0000,0000,,So when we have water flow\Nthrough, the water will flow
Dialogue: 0,0:03:01.97,0:03:06.72,Default,,0000,0000,0000,,through only if both of the\Ntabs are open. If I turn
Dialogue: 0,0:03:06.72,0:03:07.91,Default,,0000,0000,0000,,this tab off.
Dialogue: 0,0:03:09.04,0:03:13.59,Default,,0000,0000,0000,,The voter will stop here if I\Nturn this step on when I leave
Dialogue: 0,0:03:13.59,0:03:17.49,Default,,0000,0000,0000,,this tab of the water will stop\Nhere, so water still doesn't
Dialogue: 0,0:03:17.49,0:03:21.06,Default,,0000,0000,0000,,flow through an. Obviously, if\NI have both taps turned off,
Dialogue: 0,0:03:21.06,0:03:24.96,Default,,0000,0000,0000,,the water doesn't go further\Nthan here. So what are we only
Dialogue: 0,0:03:24.96,0:03:29.19,Default,,0000,0000,0000,,go through if all of these\Nsteps are on, so would have can
Dialogue: 0,0:03:29.19,0:03:33.09,Default,,0000,0000,0000,,go through only this way. Now\Nhow can we sort of summarize
Dialogue: 0,0:03:33.09,0:03:36.34,Default,,0000,0000,0000,,this information in a nice and\Nsimple visual format? That's
Dialogue: 0,0:03:36.34,0:03:37.32,Default,,0000,0000,0000,,why truth tables.
Dialogue: 0,0:03:40.51,0:03:44.17,Default,,0000,0000,0000,,Has been invented through.\NTables are simple tables which
Dialogue: 0,0:03:44.17,0:03:48.65,Default,,0000,0000,0000,,tells you what are the input\Nvalues or other possible input
Dialogue: 0,0:03:48.65,0:03:53.94,Default,,0000,0000,0000,,values that can come. What is\Nthe logic gate or what is the
Dialogue: 0,0:03:53.94,0:03:58.82,Default,,0000,0000,0000,,Boolean operation that we use\Nhere and then? What will be the
Dialogue: 0,0:03:58.82,0:04:02.49,Default,,0000,0000,0000,,end result of that Boolean\Noperation for every possible
Dialogue: 0,0:04:02.49,0:04:06.15,Default,,0000,0000,0000,,income combinations? Now let's\Nlook at the simple examples.
Dialogue: 0,0:04:06.15,0:04:08.59,Default,,0000,0000,0000,,Let's see how does the P&Q
Dialogue: 0,0:04:08.59,0:04:13.23,Default,,0000,0000,0000,,operation works. B is an input\Nqueue, is a different input.
Dialogue: 0,0:04:13.23,0:04:17.41,Default,,0000,0000,0000,,What happens if I combine them\Ntogether? What will be the
Dialogue: 0,0:04:17.41,0:04:18.93,Default,,0000,0000,0000,,common output so P.
Dialogue: 0,0:04:20.39,0:04:21.33,Default,,0000,0000,0000,,And Q.
Dialogue: 0,0:04:23.45,0:04:25.42,Default,,0000,0000,0000,,And here will be my output.
Dialogue: 0,0:04:27.54,0:04:33.36,Default,,0000,0000,0000,,Now what kind of setups can the\Ntwo taps have? While I can turn
Dialogue: 0,0:04:33.36,0:04:35.03,Default,,0000,0000,0000,,both of them on?
Dialogue: 0,0:04:37.12,0:04:41.64,Default,,0000,0000,0000,,I can turn one of them on\Nthe other one off, all in
Dialogue: 0,0:04:41.64,0:04:42.69,Default,,0000,0000,0000,,the other combination.
Dialogue: 0,0:04:43.98,0:04:46.92,Default,,0000,0000,0000,,Or I can have both\Nof them turned off.
Dialogue: 0,0:04:48.14,0:04:52.37,Default,,0000,0000,0000,,So what did we say? The water\Ncan only go through if both of
Dialogue: 0,0:04:52.37,0:04:53.58,Default,,0000,0000,0000,,the taps are on?
Dialogue: 0,0:04:54.25,0:04:58.57,Default,,0000,0000,0000,,Every other combination will\Nstop the water from flowing, so
Dialogue: 0,0:04:58.57,0:05:02.03,Default,,0000,0000,0000,,this is the truth table\Naccompanying the end.
Dialogue: 0,0:05:02.75,0:05:07.64,Default,,0000,0000,0000,,Operation. With this Boolean\Ntrip tables, you need to know
Dialogue: 0,0:05:07.64,0:05:11.60,Default,,0000,0000,0000,,them. You need to understand\Nthem because later on we'll be
Dialogue: 0,0:05:11.60,0:05:14.84,Default,,0000,0000,0000,,combining more than just one\Nsingle operation together and
Dialogue: 0,0:05:14.84,0:05:19.88,Default,,0000,0000,0000,,see what happens if we start to\Nmix them up. So this was the
Dialogue: 0,0:05:19.88,0:05:24.20,Default,,0000,0000,0000,,first one, the end operation.\NLet's have a look at the next
Dialogue: 0,0:05:24.20,0:05:28.52,Default,,0000,0000,0000,,one, which is the OR operator.\NNow the symbol for the OR
Dialogue: 0,0:05:28.52,0:05:32.48,Default,,0000,0000,0000,,operator can be this small away.\NThe opposite, the turned upside
Dialogue: 0,0:05:32.48,0:05:35.72,Default,,0000,0000,0000,,of the end or the addition\Nbecause it works.
Dialogue: 0,0:05:35.83,0:05:36.92,Default,,0000,0000,0000,,Like the audition.
Dialogue: 0,0:05:39.12,0:05:42.13,Default,,0000,0000,0000,,And if you are coming from\Nthe engineering background.
Dialogue: 0,0:05:43.32,0:05:45.88,Default,,0000,0000,0000,,You can see either this.
Dialogue: 0,0:05:48.01,0:05:51.15,Default,,0000,0000,0000,,Symbol or this symbol?
Dialogue: 0,0:05:53.79,0:05:58.01,Default,,0000,0000,0000,,For the OR gates, again it\Ntakes in at least two
Dialogue: 0,0:05:58.01,0:06:01.85,Default,,0000,0000,0000,,incoming values and gives you\None outgoing value, so at
Dialogue: 0,0:06:01.85,0:06:03.77,Default,,0000,0000,0000,,least two inputs, one output.
Dialogue: 0,0:06:05.39,0:06:07.82,Default,,0000,0000,0000,,You can think about the OR gate.
Dialogue: 0,0:06:08.37,0:06:12.00,Default,,0000,0000,0000,,As water pipes but fixed
Dialogue: 0,0:06:12.00,0:06:17.75,Default,,0000,0000,0000,,now. In a different way now\Nthese water pipes I fixed
Dialogue: 0,0:06:17.75,0:06:21.46,Default,,0000,0000,0000,,together in a parallel\Nfashion and on each branch
Dialogue: 0,0:06:21.46,0:06:23.52,Default,,0000,0000,0000,,we have got a tap.
Dialogue: 0,0:06:24.76,0:06:30.92,Default,,0000,0000,0000,,So what happens in this case?\NNow if I turn this tap off, stop
Dialogue: 0,0:06:30.92,0:06:35.76,Default,,0000,0000,0000,,the water flowing here, but I\Ndon't turn this stuff off.
Dialogue: 0,0:06:36.40,0:06:40.57,Default,,0000,0000,0000,,The water will be able to bypass\Nthat turned side and fluid flow
Dialogue: 0,0:06:40.57,0:06:44.10,Default,,0000,0000,0000,,through. Here the same the other\Nway around. And obviously if
Dialogue: 0,0:06:44.10,0:06:48.60,Default,,0000,0000,0000,,both of the tabs are open then\Nthe voter have got the choice of
Dialogue: 0,0:06:48.60,0:06:51.81,Default,,0000,0000,0000,,flowing through one or the\Nother, so the OR operation.
Dialogue: 0,0:06:52.47,0:06:56.37,Default,,0000,0000,0000,,Opposite to what the end does,\Nit only stops the water. In one
Dialogue: 0,0:06:56.37,0:07:00.27,Default,,0000,0000,0000,,case it stops the water if both\Nof the taps are turned off.
Dialogue: 0,0:07:01.57,0:07:05.51,Default,,0000,0000,0000,,So what does it look like in the\Ntruth table fashion? So again.
Dialogue: 0,0:07:07.68,0:07:12.36,Default,,0000,0000,0000,,P or Q. What are the possible\Nincome combinations and what are
Dialogue: 0,0:07:12.36,0:07:15.48,Default,,0000,0000,0000,,the possible outcome\Ncombinations of these? So again,
Dialogue: 0,0:07:15.48,0:07:17.43,Default,,0000,0000,0000,,I can have two values.
Dialogue: 0,0:07:18.27,0:07:19.71,Default,,0000,0000,0000,,Two input values P.
Dialogue: 0,0:07:20.33,0:07:20.78,Default,,0000,0000,0000,,K.
Dialogue: 0,0:07:22.02,0:07:26.99,Default,,0000,0000,0000,,So again, what are the different\Ninput combinations for these two
Dialogue: 0,0:07:26.99,0:07:29.25,Default,,0000,0000,0000,,values? The P&QA quick trick.
Dialogue: 0,0:07:29.85,0:07:37.27,Default,,0000,0000,0000,,True, true Force Force 3434.\NThis fact comes from I've
Dialogue: 0,0:07:37.27,0:07:40.24,Default,,0000,0000,0000,,got two input values.
Dialogue: 0,0:07:41.75,0:07:47.84,Default,,0000,0000,0000,,P or K, but all both of them can\Nbe true or false, so I only have
Dialogue: 0,0:07:47.84,0:07:52.49,Default,,0000,0000,0000,,got two possible switch stands.\NSo 2 to the power of two gives
Dialogue: 0,0:07:52.49,0:07:57.50,Default,,0000,0000,0000,,me 4, but two is the number of\Ninput values and two is the
Dialogue: 0,0:07:57.50,0:08:00.37,Default,,0000,0000,0000,,number of possible outcomes like\Ntrues or force.
Dialogue: 0,0:08:01.42,0:08:06.48,Default,,0000,0000,0000,,So what did we establish if\Nboth of the taps are turned
Dialogue: 0,0:08:06.48,0:08:11.55,Default,,0000,0000,0000,,on, then the voter can flow\Nthrough. If one of the taps
Dialogue: 0,0:08:11.55,0:08:16.19,Default,,0000,0000,0000,,are turned on, then the water\Ncan flow through that branch
Dialogue: 0,0:08:16.19,0:08:18.30,Default,,0000,0000,0000,,and bypass the off tab.
Dialogue: 0,0:08:19.48,0:08:24.48,Default,,0000,0000,0000,,But if both of the taps are\Nturned off than the water it
Dialogue: 0,0:08:24.48,0:08:27.95,Default,,0000,0000,0000,,stopped. So that's when this\Nthis operation is forced.
Dialogue: 0,0:08:28.72,0:08:33.56,Default,,0000,0000,0000,,So the next operation that I\Nwould like to talk about is the
Dialogue: 0,0:08:33.56,0:08:36.53,Default,,0000,0000,0000,,not operation, which sometimes\Nalso used this symbol.
Dialogue: 0,0:08:37.31,0:08:42.04,Default,,0000,0000,0000,,Sometimes this symbol and\Nsometimes it used just by a bar
Dialogue: 0,0:08:42.04,0:08:46.77,Default,,0000,0000,0000,,over the input for the pictorial\Nsymbol for the Northgate. For
Dialogue: 0,0:08:46.77,0:08:51.93,Default,,0000,0000,0000,,engineers is this it's a little\Ntriangle with a little circle at
Dialogue: 0,0:08:51.93,0:08:53.22,Default,,0000,0000,0000,,the end now.
Dialogue: 0,0:08:54.15,0:08:59.14,Default,,0000,0000,0000,,Compared with the others, the\Nnot operation only have one
Dialogue: 0,0:08:59.14,0:09:01.64,Default,,0000,0000,0000,,input and has one output.
Dialogue: 0,0:09:02.21,0:09:08.99,Default,,0000,0000,0000,,OK, so that state to wait as you\Nsomething. So if I have got just
Dialogue: 0,0:09:08.99,0:09:11.70,Default,,0000,0000,0000,,one input then that input P.
Dialogue: 0,0:09:13.27,0:09:17.79,Default,,0000,0000,0000,,Can only be true or false and\Nthen not P.
Dialogue: 0,0:09:19.30,0:09:24.51,Default,,0000,0000,0000,,But what is not true? What\Nis not true is force and
Dialogue: 0,0:09:24.51,0:09:29.28,Default,,0000,0000,0000,,what is not force is true.\NSo the not operation has
Dialogue: 0,0:09:29.28,0:09:34.06,Default,,0000,0000,0000,,got a very special role. It\Nflips it inverts it changes
Dialogue: 0,0:09:34.06,0:09:36.23,Default,,0000,0000,0000,,the input to its opposite.
Dialogue: 0,0:09:37.70,0:09:40.34,Default,,0000,0000,0000,,The next simple operation\Nis the X or.
Dialogue: 0,0:09:41.85,0:09:47.99,Default,,0000,0000,0000,,Which has got this symbol, so it\Ndoesn't have that many symbol as
Dialogue: 0,0:09:47.99,0:09:53.18,Default,,0000,0000,0000,,the not. So that's easier. And\Nthe exors pictorial symbol for
Dialogue: 0,0:09:53.18,0:09:54.59,Default,,0000,0000,0000,,joining as circuit.
Dialogue: 0,0:09:55.72,0:09:57.52,Default,,0000,0000,0000,,Is the OR gate?
Dialogue: 0,0:10:00.40,0:10:04.86,Default,,0000,0000,0000,,But with an extra leg added to\Nit so it can take again at least
Dialogue: 0,0:10:04.86,0:10:08.72,Default,,0000,0000,0000,,two inputs. Or if we use the\Nalternative way of the X or.
Dialogue: 0,0:10:10.65,0:10:11.69,Default,,0000,0000,0000,,And it would look.
Dialogue: 0,0:10:12.42,0:10:13.50,Default,,0000,0000,0000,,Something like that.
Dialogue: 0,0:10:14.61,0:10:20.01,Default,,0000,0000,0000,,OK, now this is called the\Naxle operation because it's
Dialogue: 0,0:10:20.01,0:10:20.55,Default,,0000,0000,0000,,exclusive.
Dialogue: 0,0:10:22.16,0:10:22.63,Default,,0000,0000,0000,,Or
Dialogue: 0,0:10:23.83,0:10:29.18,Default,,0000,0000,0000,,so it's exclusively one or the\Nother input, so the xclusive
Dialogue: 0,0:10:29.18,0:10:35.01,Default,,0000,0000,0000,,or the X or operation filters\Nout the input values when the
Dialogue: 0,0:10:35.01,0:10:41.81,Default,,0000,0000,0000,,inputs are the same. So what\Ndo I mean by that? If I have
Dialogue: 0,0:10:41.81,0:10:43.27,Default,,0000,0000,0000,,got inputs P&Q?
Dialogue: 0,0:10:45.39,0:10:49.56,Default,,0000,0000,0000,,What will the acts or do\Nto them?
Dialogue: 0,0:10:51.79,0:10:57.02,Default,,0000,0000,0000,,So again, be can be true\Nto force force and Q is
Dialogue: 0,0:10:57.02,0:10:58.77,Default,,0000,0000,0000,,true force three force.
Dialogue: 0,0:10:59.95,0:11:04.50,Default,,0000,0000,0000,,So exclusive, or if the inputs\Nare the same, which is this
Dialogue: 0,0:11:04.50,0:11:09.42,Default,,0000,0000,0000,,case? Because both of them are\Ntrue. The Exor Gate gives you a
Dialogue: 0,0:11:09.42,0:11:13.22,Default,,0000,0000,0000,,4th signal. Basically the axle\Ngates stops the signal going
Dialogue: 0,0:11:13.22,0:11:18.14,Default,,0000,0000,0000,,through. If one is to the other\None is forced then that's when
Dialogue: 0,0:11:18.14,0:11:22.31,Default,,0000,0000,0000,,the signal can go through and\Nagain because force enforces the
Dialogue: 0,0:11:22.31,0:11:26.48,Default,,0000,0000,0000,,same input value that the EXOR\Ngate stops your signal going
Dialogue: 0,0:11:26.48,0:11:30.27,Default,,0000,0000,0000,,through. And remember that I\Nmentioned at the beginning of
Dialogue: 0,0:11:30.27,0:11:34.58,Default,,0000,0000,0000,,this video. These are based on\Nthe electric circuits and then
Dialogue: 0,0:11:34.58,0:11:38.50,Default,,0000,0000,0000,,you wanted to manipulate at the\Nvery, very early stages or
Dialogue: 0,0:11:38.50,0:11:42.06,Default,,0000,0000,0000,,lippit stages of computing you\Nwanted to manipulate where the
Dialogue: 0,0:11:42.06,0:11:45.26,Default,,0000,0000,0000,,electrical signal goes doesn't\Ngo through here doesn't go
Dialogue: 0,0:11:45.26,0:11:48.47,Default,,0000,0000,0000,,through that you wanted to\Nmanipulate and filter out
Dialogue: 0,0:11:48.47,0:11:52.38,Default,,0000,0000,0000,,certain inputs in favor of other\Ninputs. So these different gates
Dialogue: 0,0:11:52.38,0:11:56.66,Default,,0000,0000,0000,,give you that kind of option of\Nturning them around. Saying, I
Dialogue: 0,0:11:56.66,0:12:00.57,Default,,0000,0000,0000,,don't want this input, I want\Nthat that input combination to
Dialogue: 0,0:12:00.57,0:12:02.35,Default,,0000,0000,0000,,go through and nothing else.
Dialogue: 0,0:12:03.53,0:12:06.72,Default,,0000,0000,0000,,There are a couple of more\Noperations that I would like
Dialogue: 0,0:12:06.72,0:12:09.33,Default,,0000,0000,0000,,to talk about. These are\Nslightly more complicated. I
Dialogue: 0,0:12:09.33,0:12:12.81,Default,,0000,0000,0000,,can't really give you any nice\Nand simple example of why they
Dialogue: 0,0:12:12.81,0:12:16.58,Default,,0000,0000,0000,,work in here. We just have to\Nlearn that this is the way
Dialogue: 0,0:12:16.58,0:12:19.77,Default,,0000,0000,0000,,that they work, so one of them\Nis that you've done.
Dialogue: 0,0:12:22.05,0:12:25.05,Default,,0000,0000,0000,,And the symbol for that\Nis this forward error.
Dialogue: 0,0:12:26.44,0:12:30.35,Default,,0000,0000,0000,,So again. I've got inputs P&Q.
Dialogue: 0,0:12:31.32,0:12:35.22,Default,,0000,0000,0000,,And then what will be\Nthe Alpha output of the
Dialogue: 0,0:12:35.22,0:12:37.17,Default,,0000,0000,0000,,P IF then Q operation?
Dialogue: 0,0:12:39.62,0:12:46.59,Default,,0000,0000,0000,,So true true Force force\Nthree force, three force.
Dialogue: 0,0:12:48.03,0:12:51.06,Default,,0000,0000,0000,,Sometimes this also\Ncalled the implies.
Dialogue: 0,0:12:53.47,0:12:57.20,Default,,0000,0000,0000,,So true implies true, that is
Dialogue: 0,0:12:57.20,0:13:04.34,Default,,0000,0000,0000,,true. But true cannot imply\Nforce, so this one is force
Dialogue: 0,0:13:04.34,0:13:06.59,Default,,0000,0000,0000,,force can imply true.
Dialogue: 0,0:13:08.15,0:13:11.29,Default,,0000,0000,0000,,And force can imply force\Nthat's true. Again, this is
Dialogue: 0,0:13:11.29,0:13:14.43,Default,,0000,0000,0000,,probably going to be the most\Ndifficult gate to understand
Dialogue: 0,0:13:14.43,0:13:18.20,Default,,0000,0000,0000,,why this works. You just have\Nto learn the truth tables, and
Dialogue: 0,0:13:18.20,0:13:21.65,Default,,0000,0000,0000,,once you know the truth\Ntables, you can apply it to
Dialogue: 0,0:13:21.65,0:13:22.91,Default,,0000,0000,0000,,any kind of combinations.
Dialogue: 0,0:13:25.07,0:13:29.31,Default,,0000,0000,0000,,And the last operation that I\Nwould like to talk about is that
Dialogue: 0,0:13:29.31,0:13:30.61,Default,,0000,0000,0000,,if and only if.
Dialogue: 0,0:13:33.13,0:13:36.90,Default,,0000,0000,0000,,And the symbol for that is\Nan arrow that goes both
Dialogue: 0,0:13:36.90,0:13:40.68,Default,,0000,0000,0000,,ways. So if I have got the\Ntwo inputs again P&Q.
Dialogue: 0,0:13:42.84,0:13:47.57,Default,,0000,0000,0000,,The P if and only Q\Nwill work this way.
Dialogue: 0,0:13:49.13,0:13:55.02,Default,,0000,0000,0000,,33443434.
Dialogue: 0,0:13:57.24,0:13:59.44,Default,,0000,0000,0000,,This one is only true.
Dialogue: 0,0:14:00.42,0:14:05.49,Default,,0000,0000,0000,,If both inputs are the same, so\Ntrue and true are the same, so
Dialogue: 0,0:14:05.49,0:14:09.47,Default,,0000,0000,0000,,this will be true. True annefors\Nare different, so the output
Dialogue: 0,0:14:09.47,0:14:14.54,Default,,0000,0000,0000,,will be force same for the third\Nright and for some for side the
Dialogue: 0,0:14:14.54,0:14:19.97,Default,,0000,0000,0000,,same. So this is true in here.\NNow if you look at this one and
Dialogue: 0,0:14:19.97,0:14:24.31,Default,,0000,0000,0000,,if you remember the X or you can\Nsupport that these two
Dialogue: 0,0:14:24.31,0:14:29.02,Default,,0000,0000,0000,,operations if and only if an the\NX or are doing exactly the
Dialogue: 0,0:14:29.02,0:14:30.83,Default,,0000,0000,0000,,opposite in this using this.
Dialogue: 0,0:14:30.88,0:14:37.31,Default,,0000,0000,0000,,Operation I can filter out the\Nsame input values and stop the
Dialogue: 0,0:14:37.31,0:14:38.92,Default,,0000,0000,0000,,different input values.
Dialogue: 0,0:14:40.00,0:14:43.13,Default,,0000,0000,0000,,So that's again a very useful\Noperation to have.
Dialogue: 0,0:14:46.12,0:14:50.75,Default,,0000,0000,0000,,This short video was intended to\Nexpose you to the basics of the
Dialogue: 0,0:14:50.75,0:14:54.66,Default,,0000,0000,0000,,Boolean logic or digital logic\Nand show you had the truth.
Dialogue: 0,0:14:54.66,0:14:58.94,Default,,0000,0000,0000,,Tables can be built up and what\Nare the most commonly used
Dialogue: 0,0:14:58.94,0:15:03.21,Default,,0000,0000,0000,,operations to be able to follow\Nup on digital logic? You will
Dialogue: 0,0:15:03.21,0:15:07.84,Default,,0000,0000,0000,,need to be able to know this by\Nheart, so these are different
Dialogue: 0,0:15:07.84,0:15:12.11,Default,,0000,0000,0000,,operations that every time you\Nneed to apply them you will be
Dialogue: 0,0:15:12.11,0:15:15.67,Default,,0000,0000,0000,,have to be very, very confident\Nknowing these operations how
Dialogue: 0,0:15:15.67,0:15:19.18,Default,,0000,0000,0000,,they work. What they do? What\Nkind of inputs they let
Dialogue: 0,0:15:19.18,0:15:22.52,Default,,0000,0000,0000,,through an? What kind? What\Nkind of inputs they stop from
Dialogue: 0,0:15:22.52,0:15:25.56,Default,,0000,0000,0000,,going through? And again, as I\Nmentioned at the beginning,
Dialogue: 0,0:15:25.56,0:15:28.60,Default,,0000,0000,0000,,this is all coming from the\Nbasic principles that went
Dialogue: 0,0:15:28.60,0:15:31.64,Default,,0000,0000,0000,,first. Human started team when\Nthe computers they build them
Dialogue: 0,0:15:31.64,0:15:33.46,Default,,0000,0000,0000,,together from very tiny basic\Ncircuits.