[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:18.72,0:00:22.69,Default,,0000,0000,0000,,Welcome to the next video. In\Nthe Boolean series. In this
Dialogue: 0,0:00:22.69,0:00:27.02,Default,,0000,0000,0000,,video I'm going to show you what\NBoolean expressions are and how
Dialogue: 0,0:00:27.02,0:00:30.99,Default,,0000,0000,0000,,we can use the laws of logic to\Nmake them simpler.
Dialogue: 0,0:00:31.96,0:00:38.16,Default,,0000,0000,0000,,But I've shown you a lot of\NLowe's and I've shown you a lot
Dialogue: 0,0:00:38.16,0:00:41.71,Default,,0000,0000,0000,,of operations, but what are\Nactually Boolean expressions?
Dialogue: 0,0:00:41.71,0:00:45.25,Default,,0000,0000,0000,,But Boolean expressions are\Nbasically just input values.
Dialogue: 0,0:00:45.25,0:00:49.68,Default,,0000,0000,0000,,Peace, QS, and Rs combined\Ntogether with all these logical
Dialogue: 0,0:00:49.68,0:00:52.78,Default,,0000,0000,0000,,operations, so different letters\Nrepresenting different input
Dialogue: 0,0:00:52.78,0:00:56.32,Default,,0000,0000,0000,,values and combined together\Nwith these logical operations
Dialogue: 0,0:00:56.32,0:00:58.54,Default,,0000,0000,0000,,just like in algebra for
Dialogue: 0,0:00:58.54,0:01:05.03,Default,,0000,0000,0000,,example. P&Q\NXRR is a Boolean expression,
Dialogue: 0,0:01:05.03,0:01:08.49,Default,,0000,0000,0000,,another somewhat more\Ncomplicated Boolean expression
Dialogue: 0,0:01:08.49,0:01:10.79,Default,,0000,0000,0000,,is something like P&Q.
Dialogue: 0,0:01:11.65,0:01:13.95,Default,,0000,0000,0000,,Call
Dialogue: 0,0:01:15.04,0:01:22.00,Default,,0000,0000,0000,,Not Q&R Or\NP if then K.
Dialogue: 0,0:01:23.62,0:01:25.60,Default,,0000,0000,0000,,And not Q.
Dialogue: 0,0:01:26.31,0:01:31.29,Default,,0000,0000,0000,,If an only if R, so whichever\Noperation you want to put
Dialogue: 0,0:01:31.29,0:01:35.86,Default,,0000,0000,0000,,together, and then how many\Ninputs are there, it is again
Dialogue: 0,0:01:35.86,0:01:39.59,Default,,0000,0000,0000,,different for each expressions.\NAs I mentioned, these different
Dialogue: 0,0:01:39.59,0:01:42.91,Default,,0000,0000,0000,,expressions will carry out\Ndifferent instructions for the
Dialogue: 0,0:01:42.91,0:01:45.40,Default,,0000,0000,0000,,computer, so the computer can do
Dialogue: 0,0:01:45.40,0:01:49.23,Default,,0000,0000,0000,,different things. And allow\Nthrough certain input
Dialogue: 0,0:01:49.23,0:01:53.10,Default,,0000,0000,0000,,combinations and stop certain\Ninput combinations from going
Dialogue: 0,0:01:53.10,0:01:55.04,Default,,0000,0000,0000,,through in the circuit.
Dialogue: 0,0:01:56.52,0:02:01.43,Default,,0000,0000,0000,,Now let's talk a little bit\Nabout the rules of the brackets.
Dialogue: 0,0:02:01.43,0:02:07.56,Default,,0000,0000,0000,,So if I have got the expression\Nof not P&Q, and if I have got
Dialogue: 0,0:02:07.56,0:02:12.47,Default,,0000,0000,0000,,the expression of not P&Q, what\Nis the difference in here? What
Dialogue: 0,0:02:12.47,0:02:16.97,Default,,0000,0000,0000,,am I doing by placing the\Nbracket? Well, just as in
Dialogue: 0,0:02:16.97,0:02:20.24,Default,,0000,0000,0000,,algebra by pressing a bracket\Nsomewhere, I'm emphasizing
Dialogue: 0,0:02:20.24,0:02:25.15,Default,,0000,0000,0000,,priority in this expression. The\Nknot is only applied to pee and
Dialogue: 0,0:02:25.15,0:02:27.60,Default,,0000,0000,0000,,to be able to calculate the.
Dialogue: 0,0:02:27.66,0:02:30.48,Default,,0000,0000,0000,,Overall, output of this\Nexpression. I need to
Dialogue: 0,0:02:30.48,0:02:34.35,Default,,0000,0000,0000,,calculate not P and combine it\Ntogether with the key using
Dialogue: 0,0:02:34.35,0:02:38.22,Default,,0000,0000,0000,,the end operation as opposed\Nto hear hear the bracket is
Dialogue: 0,0:02:38.22,0:02:42.80,Default,,0000,0000,0000,,applied to the P&Q. So I need\Nto calculate the P&Q 1st and
Dialogue: 0,0:02:42.80,0:02:47.02,Default,,0000,0000,0000,,then the note is applied to\Nthe all of it with the
Dialogue: 0,0:02:47.02,0:02:51.24,Default,,0000,0000,0000,,bracket. So once I found the\NP&Q output values then I need
Dialogue: 0,0:02:51.24,0:02:55.12,Default,,0000,0000,0000,,to invert them. I need to\Napply the not operation to
Dialogue: 0,0:02:55.12,0:02:59.69,Default,,0000,0000,0000,,those output values to get to\Nthe whole output so it will be
Dialogue: 0,0:02:59.69,0:03:02.16,Default,,0000,0000,0000,,very different in the two\Ndifferent cases.
Dialogue: 0,0:03:03.28,0:03:07.09,Default,,0000,0000,0000,,Similarly, if I have got P&Q.
Dialogue: 0,0:03:08.26,0:03:14.76,Default,,0000,0000,0000,,X or R or P&QX or R. The bracket\Ntells me what I need to do
Dialogue: 0,0:03:14.76,0:03:19.22,Default,,0000,0000,0000,,first. Here I need to use the\Nend operation and combined
Dialogue: 0,0:03:19.22,0:03:23.28,Default,,0000,0000,0000,,together P&Q then find the\Noutput and combined it together
Dialogue: 0,0:03:23.28,0:03:28.56,Default,,0000,0000,0000,,with the I using the axe or\Nwhile in this case is the
Dialogue: 0,0:03:28.56,0:03:33.43,Default,,0000,0000,0000,,opposite way around. I need to\Nuse the exit gate combined Q&R
Dialogue: 0,0:03:33.43,0:03:37.90,Default,,0000,0000,0000,,together 1st and then use the\Nend operation to combine output
Dialogue: 0,0:03:37.90,0:03:41.98,Default,,0000,0000,0000,,from here. Which P to get to\Nthe final output of the
Dialogue: 0,0:03:41.98,0:03:42.91,Default,,0000,0000,0000,,overall Boolean expression.
Dialogue: 0,0:03:44.05,0:03:49.80,Default,,0000,0000,0000,,Now the last thing I'd like to\Nshow you in this video is how we
Dialogue: 0,0:03:49.80,0:03:54.01,Default,,0000,0000,0000,,can use these laws of logic to\Nreduce the Boolean expressions.
Dialogue: 0,0:03:54.01,0:04:00.14,Default,,0000,0000,0000,,So I have this expression not P\Nor not Q. So how can I use the
Dialogue: 0,0:04:00.14,0:04:04.73,Default,,0000,0000,0000,,lose of logic to reduce this\Nexpression? Now I can use the
Dialogue: 0,0:04:04.73,0:04:09.33,Default,,0000,0000,0000,,Morgan low to distribute the not\Nover the bracket. So what does
Dialogue: 0,0:04:09.33,0:04:15.07,Default,,0000,0000,0000,,the De Morgan do? I can break it\Nup into not P and not not.
Dialogue: 0,0:04:15.23,0:04:20.91,Default,,0000,0000,0000,,Cute and then I can use the\Ndouble negation and applied the
Dialogue: 0,0:04:20.91,0:04:24.69,Default,,0000,0000,0000,,not not key so that gives me not
Dialogue: 0,0:04:24.69,0:04:30.84,Default,,0000,0000,0000,,P&Q. Well, I think he would like\Nto agree with me that instead of
Dialogue: 0,0:04:30.84,0:04:33.98,Default,,0000,0000,0000,,this bracketed expression, this\Nexpression is rather similar.
Dialogue: 0,0:04:36.05,0:04:38.91,Default,,0000,0000,0000,,One more example, not.
Dialogue: 0,0:04:39.56,0:04:41.33,Default,,0000,0000,0000,,Key or P?
Dialogue: 0,0:04:43.91,0:04:44.39,Default,,0000,0000,0000,,Or
Dialogue: 0,0:04:47.17,0:04:53.98,Default,,0000,0000,0000,,Not P&Q What I have\Nhere is key or P and I have
Dialogue: 0,0:04:53.98,0:04:59.38,Default,,0000,0000,0000,,here not P&Q. So I have got\Nthe same things in here but I
Dialogue: 0,0:04:59.38,0:05:04.40,Default,,0000,0000,0000,,have got them in the opposite\Norder so why can do? First I
Dialogue: 0,0:05:04.40,0:05:09.03,Default,,0000,0000,0000,,can apply the commutative low\Nand bring them up in the same
Dialogue: 0,0:05:09.03,0:05:10.19,Default,,0000,0000,0000,,kind of order.
Dialogue: 0,0:05:16.01,0:05:21.16,Default,,0000,0000,0000,,Then what I can use next is the\NMorgan loads to distribute the
Dialogue: 0,0:05:21.16,0:05:26.31,Default,,0000,0000,0000,,not inside the bracket. So that\Ngives me not P and not Q.
Dialogue: 0,0:05:29.01,0:05:36.36,Default,,0000,0000,0000,,Or Not P&Q now what\NI have in here now. It's like
Dialogue: 0,0:05:36.36,0:05:38.47,Default,,0000,0000,0000,,in algebra you spot.
Dialogue: 0,0:05:38.99,0:05:41.56,Default,,0000,0000,0000,,That the first term here.
Dialogue: 0,0:05:42.78,0:05:47.41,Default,,0000,0000,0000,,Is the same, so you can do\Nsomething called in algebra,
Dialogue: 0,0:05:47.41,0:05:52.04,Default,,0000,0000,0000,,factorization and in this case I\Ncan use the backwards operation.
Dialogue: 0,0:05:52.04,0:05:56.67,Default,,0000,0000,0000,,The backwards version of the\Ndistributive law so I can bring
Dialogue: 0,0:05:56.67,0:05:58.36,Default,,0000,0000,0000,,out the note P.
Dialogue: 0,0:05:59.64,0:06:01.53,Default,,0000,0000,0000,,And the end.
Dialogue: 0,0:06:02.26,0:06:05.80,Default,,0000,0000,0000,,And what remains is the not
Dialogue: 0,0:06:05.80,0:06:07.74,Default,,0000,0000,0000,,Q. Or key.
Dialogue: 0,0:06:09.20,0:06:11.35,Default,,0000,0000,0000,,Now what do I know about not Q
Dialogue: 0,0:06:11.35,0:06:16.84,Default,,0000,0000,0000,,or key? But I know about Nokia\Nor cubes that that is always
Dialogue: 0,0:06:16.84,0:06:21.85,Default,,0000,0000,0000,,true because it doesn't matter\Nwhich not Q or Q is force, the
Dialogue: 0,0:06:21.85,0:06:26.47,Default,,0000,0000,0000,,other will be always true and\Ntrue. Or force always gives you
Dialogue: 0,0:06:26.47,0:06:31.09,Default,,0000,0000,0000,,true. So this is also the same\Nas not P and true.
Dialogue: 0,0:06:33.09,0:06:33.80,Default,,0000,0000,0000,,And.
Dialogue: 0,0:06:35.33,0:06:37.09,Default,,0000,0000,0000,,Not P and true.
Dialogue: 0,0:06:38.02,0:06:43.12,Default,,0000,0000,0000,,That is always equal to not pee.\NI can apply the identity law
Dialogue: 0,0:06:43.12,0:06:48.21,Default,,0000,0000,0000,,here, which states that P and\Ntwo is always P for the special
Dialogue: 0,0:06:48.21,0:06:53.31,Default,,0000,0000,0000,,case of not PN 2 is always not\Npaying. So this long complicated
Dialogue: 0,0:06:53.31,0:06:56.44,Default,,0000,0000,0000,,expression is actually nothing\Nelse but not P.
Dialogue: 0,0:06:57.23,0:07:01.99,Default,,0000,0000,0000,,I hope that you now have a\Ngood idea of how to use the
Dialogue: 0,0:07:01.99,0:07:05.05,Default,,0000,0000,0000,,lose of logic to simplify\NBoolean expressions in the
Dialogue: 0,0:07:05.05,0:07:09.13,Default,,0000,0000,0000,,next slide you will have some\Nquestions to allow you to do
Dialogue: 0,0:07:09.13,0:07:13.21,Default,,0000,0000,0000,,some practice on your own and\Nyou will find the answers to
Dialogue: 0,0:07:13.21,0:07:14.57,Default,,0000,0000,0000,,these questions shortly after.
Dialogue: 0,0:07:16.19,0:07:18.22,Default,,0000,0000,0000,,So these are the practice\Nquestions.
Dialogue: 0,0:07:24.27,0:07:25.89,Default,,0000,0000,0000,,And here are the answers.