Slide Show. 14 January 201614 January 201614 January 2016 1st Year, Chapter 4 2 Boolean Algebra 1847...
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Transcript of Slide Show. 14 January 201614 January 201614 January 2016 1st Year, Chapter 4 2 Boolean Algebra 1847...
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April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 22
Boolean Algebra 1847Boolean Algebra 1847Boolean Algebra 1847Boolean Algebra 1847
George BooleGeorge BooleGeorge BooleGeorge Boole
April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 33
Aa¨vq 4 : wWwRUvj jwRKAa¨vq 4 : wWwRUvj jwRK
eywjqvb ¯^Ztwm×eywjqvb ¯^Ztwm×
11 00 ++ 00 == 00
22 00 ++ 11 == 11
33 11 ++ 00 == 11
44 11 ++ 11 == 11
OR OperationOR Operation
11 00 .. 00 == 00
22 00 .. 11 == 00
33 11 .. 00 == 00
44 11 .. 11 == 11
AND OperationAND Operation
April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 44
eywjqvb Dccv`¨eywjqvb Dccv`¨
AA 01 AA
AAA 11A
00. A
0. AA
AAA .AA 1.
1
2
3
4
5
6
7
8
April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 55
eywjqvb Dccv`¨eywjqvb Dccv`¨
09
10
11
))(( CABABCA
wW giM¨vb Dccv`¨wW giM¨vb Dccv`¨BABA .)(
BABA ).(
12 AA
April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 66
m~Î cÖgvbm~Î cÖgvb
If A=1 Then Ā=0, A+Ā= 1+0=1
1 AA
If A=0 Then Ā=1, A+Ā= 0+1=1
A+Ā= 1 ; Proved
April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 77
m~Î cÖgvbm~Î cÖgvb
R.H.S
))(( CABABCA
= (A+B)(A+C)
= A+AB+AC+BC
= A(1+B+C)+BC
= A+BC
= L.H.S
R.H.S= L.H.S, Proved
[A.A=A]
[1+A=1]
April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 88
divmx MwYZwe` wW divmx MwYZwe` wW giM¨vbgiM¨vb
BABA .)(
BABA ).(
April 21, 2023April 21, 2023 1st Year, Chapter 41st Year, Chapter 4 99
wW giM¨vb Dccv`¨ wW giM¨vb Dccv`¨ cÖgvbcÖgvbBABA .)( BABA ).(
AA BB
00 00
00 11
11 00
11 11
AA BB
11 11
11 00
00 11
00 00
A+BA+B
00
11
11
11
A+BA+B
11
00
00
00
A+BA+B
11
11
11
00
ABAB
00
00
00
11
ABAB
11
11
11
00
ABAB
11
00
00
00
