Guru
05-15-2010, 03:32 AM
Question 1: [marks: 10]
Simplify the following Boolean expressions, using Boolean Algebraic rules:
ABC' + A'BC + ABC + A'BC'
= BC' (A+A')+BC' (A+A') //*Because A+A'=1
So,
=BC' (1)BC' (1)
=B(C'+C)=B(1)
=B
(BC' + A'D) (AB'+ CD')
=BC'AB'+BC'CD'+A'DAB'+A'DCD'
=C'ABB'+BD'C'C+DB'AA'+A'CDD'
BY RULE A.A'=0
SO
BB'=0, CC'=0 , AA'=0 AND DD'=0
Answer =0
Question 2: [marks: 10]
Simplify the following Boolean functions, using Karnuagh maps:
F(A,B,C,D) = ∑ (3,7,11,13,14,15)
Solution:
Since the function has four variables so,a four variable map must be used.The minterms listed in the sum are marked by 1’s in the map.
192
For Solution In Doc file see the attachment below
193
Simplify the following Boolean expressions, using Boolean Algebraic rules:
ABC' + A'BC + ABC + A'BC'
= BC' (A+A')+BC' (A+A') //*Because A+A'=1
So,
=BC' (1)BC' (1)
=B(C'+C)=B(1)
=B
(BC' + A'D) (AB'+ CD')
=BC'AB'+BC'CD'+A'DAB'+A'DCD'
=C'ABB'+BD'C'C+DB'AA'+A'CDD'
BY RULE A.A'=0
SO
BB'=0, CC'=0 , AA'=0 AND DD'=0
Answer =0
Question 2: [marks: 10]
Simplify the following Boolean functions, using Karnuagh maps:
F(A,B,C,D) = ∑ (3,7,11,13,14,15)
Solution:
Since the function has four variables so,a four variable map must be used.The minterms listed in the sum are marked by 1’s in the map.
192
For Solution In Doc file see the attachment below
193