Page 65 - Computer science 868 Class 12
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49. Convert the following Boolean expression into its canonical POS form: [ISC 2017]
F(A, B, C) = (B + C').(A' + B)
Ans. F(A, B, C) = (B + C').(A' + B)
= (B + C'+ 0) . (A'+ B + 0)
= (B+C'+(A.A')).(A'+B+(C.C')) [Because A.A' = 0 and C.C' = 0]
= (A+B+C').(A'+B+C').(A'+B+C).(A'+B+C')
50. Prove the Boolean expression using Boolean laws. Also, mention the law used at each step. [ISC 2017]
F = (x' + z) + [(y' + z).(x' + y)]' = 1
Ans. F = (x' + z) + [(y' + z).(x' + y)]' = 1
= x' + z + (y' + z)' + (x’ + y)'
= x' + z + (y')' z' + (x')' y' [De Morgan’s Law]
= x' + z + yz' + xy' [Double Negation]
= x' + xy' + z + yz' [a + a'b = a + b]
= x' + y' + z + y
= x' + z + y' + y [Complement Law: a + a' = 1]
= x' + z + 1
= 1
51. Define maxterms and minterms. Find the maxterm and minterm when: [ISC 2017]
P = 0, Q = 1, R = 1 and S = 0
Ans. Maxterm can be defined as the sum terms of all the variables present in the expression both in complemented and normal forms.
Minterm can be defined as the product terms of all the variables present in the expression both in complemented and normal
forms.
Given - P = 0, Q = 1, R = 1 and S = 0
P Q R S Maxterm Minterm
0 1 1 0 P+Q'+R'+S P'.Q.R.S'
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Boolean Algebra 63

