3 - Simplification of Boolean Expression using Boolean Theorem(1) - video Dailymotion

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Transcript

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

3 - Simplification of Boolean Expression using Boolean Theorem(1)

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