00:00Suppose we say x is equal to a bar, b bar, c bar plus a, b bar, c bar.
00:09Then we say hold bar.
00:11So we say this expression, this Boolean expression, we say simplify.
00:17So we say we use Demorgan's theorem.
00:21So we say d is a bar, b bar, c.
00:25So we say d is a bar plus a, b bar, c bar.
00:31Then we say d is a bar.
00:33Then we say d is a morgan's theorem.
00:37So we say d is a morgan's theorem in this theorem.
00:41So we say this expression,
00:44a is equal to a bar.
00:46So this expression is equal to a bar.
00:48So we say this expression,
00:51a double bar,
00:54b double bar, c bar.
00:56And then mask we say,
01:00we say plus.
01:02So we say plus is a product.
01:05And a bar plus b double bar plus c double bar.
01:10We say plus is a product.
01:13So we say d morgan's theorem.
01:16We say positive is a product.
01:19And positive is a product.
01:22So then our calculation is going to be simple.
01:24A double bar is equal to a bar.
01:27Then b double bar is equal to b.
01:29And c is a single bar dot.
01:32A bar plus b plus c.
01:36Because b bar is equal to b.
01:39C double bar is equal to c.
01:42So that's all the answer.
01:44So a one of the math asked by example.
01:50Simplify the following boolean expression using boolean algebra.
01:56Suppose given number as a plus b got a plus b bar.
02:01This is a simple fact.
02:04So first of all,
02:06I am going to do this.
02:08A into a plus a into b bar plus b into a.
02:17So now I am going to do this.
02:18A into b bar.
02:22B into b bar.
02:24So overall,
02:24a into a.
02:26A into a,
02:26b into a is equal to 9 or a.
02:29So I am going to write a value.
02:31So a into a plus a,
02:34plus a into b,
02:36plus a into b,
02:38plus a into b,
02:40plus b into b bar.
02:43B x b bar a bar
02:57B bar a bar plus B
02:59then overall
03:00my more example
03:02a bar equals one
03:05b plus b bar is equals one
03:08into a
03:11A into 1
03:13A into 1 is equal to A
03:18So overall simplification
03:21A expression into simple formula A
03:25Second A plus B plus A B C plus A B C plus A B C plus A B C
03:33This is simple formula
03:36First of all, what do we do
03:38Let's say A B C
03:41A B C bar
03:44A B C bar
03:46A B C bar
03:48C plus C bar
03:50Plus A B bar C
03:52We have to write
03:54Then A B dot
03:58A plus A bar is equal to 1
04:02Then C plus C bar is equal to 1
04:05Plus A B bar C
04:09Then A common
04:11B plus B bar C
04:15We have to write
04:16We have to write
04:17The theorem
04:18That is
04:19X plus X bar Y
04:21Is equal to X plus Y
04:23So we have to write
04:24B X Y plus
04:25X bar B bar
04:27Into Y
04:29C
04:30Then we write
04:31We have to write
04:32X bar B bar C
04:33X plus Y bar
04:35We have to write
04:37We have to write
04:38B plus C
04:39So we have to write
04:40A plus A into B plus C
04:44X plus X Y is equal to X
04:48So we have to write
04:49So we have to write
04:50Bell B bar C
04:51So we have to write
04:52X plus Y
04:53Is equal to
04:54I have to write
04:55X
04:56Into 1
04:57Is equal to X
04:59So X
05:00In our way
05:02X into 1
05:03Plus
05:04XY
05:05What we have to write
05:06Is a value
05:07Then
05:08X
05:09Into 1
05:10Plus
05:11XY
05:12This is a value
05:13X
05:14so I'm not Janije x into y plus z x into y plus z it's a free button activity xy
05:25plus xz so xy plus xz check on the economy x only then no answer
05:36y 1 plus y by 1 plus y give y plus on a directory then y plus 1 is equal to 1
05:44then x in into 1 is equal to x that proves
