## Boolean-Expression

 Question 1

Which one of the following is NOT a valid identity?

 A (x + y) ⊕ z = x ⊕ (y + z) B (x ⊕ y) ⊕ z = x ⊕ (y ⊕ z) C x ⊕ y = x + y, if xy = 0 D x ⊕ y = (xy + x'y')'
Digital-Logic-Design       Boolean-Expression       GATE 2019       Video-Explanation
Question 1 Explanation:
Let x=1, y=1, z=0.
(x+y) ⊕ z = (1+1)⊕ 0 = 1 ⊕ 0 = 1
x ⊕ (y+z) = 1⊕(1+0) = 1 ⊕ 1 = 0
So,
(x+y) ⊕ z ≠ x ⊕ (y+z)
 Question 2
The value of a1 + a1.b1 + b1 + a + 0 is :
 A a1 + b1 B b1 + a C 1 D 0
Digital-Logic-Design       Boolean-Expression       TNPSC-2017-Polytechnic-CS
Question 2 Explanation:
a’ + a’b’ + b’ + a + 0
= a’(a+b’) + b’ + a + 0
= a’ + a + b’ (∵1+x=1)
= 1+b (∵ x’+x=1)
= 1 (∵ 1+x=1)
 Question 3

According to boolean law: (A')' = ?

 A 0 B A C (A')' D 1
Digital-Logic-Design       Boolean-Expression       CIL 2020
Question 3 Explanation:
Complement of any variable even times will give the same variable. And complement of any variable odd times will give the complement of that variable.
Since in the question complement of variable is done 2 times which is even, so will give the same variable.
 Question 4

For following logic diagram which expression is true?

 A (AB) (AB.)' B ((A'B'),(AB.))' C ((A'B')+(AB.))' D (AB)'.AB
Digital-Logic-Design       Boolean-Expression       CIL 2020
 Question 5

Which of the following is equivalent to the boolean expression given below?

` A+A'.B+A.B' `
 A A+B B A+B' C B+A' D B'+A'
Digital-Logic-Design       Boolean-Expression       CIL 2020
Question 5 Explanation:
A + A’B + AB’
= (A + A’) (A + B) + AB’
= 1 ∙ (A + B) + AB’ (∴ A + A’ = 1)
= (A + B) + AB’
= A + (B + A) (B + B’) (∴ B + B’ = 1)
= A + (B + A) ∙ 1
= A + B + A
= A + B
 Question 6

Canonical SOP form of logic expression consists of only ____

 A Maxterms B Laterals C Cell D Minterms
Digital-Logic-Design       Boolean-Expression       CIL 2020
Question 6 Explanation:
There are 2 steps to derive the Canonical Sum of Products Form from its truth table.
1. A Minterm is a product (AND) term containing all input variables of the function in either true or complemented form. A variable appears in complemented form ~X if it is a 0 in the row of the truth-table, and as a true form X if it appears as a 1 in the row.
Examples
A=0, B=1, C=0 -> ~A*B*~C
A=1. B=0, C=0 -> A*~B*~C
2. The canonical form is obtained by taking the sum (OR) of the minterm of the rows where a 1 appears in the output.
 Question 7
The simplified SOP(Sum of Products) form of the boolean expression (P+Q’+R’) (P+Q’+R) (P+Q+R’) is
 A (P’ Q + R) B (P + Q’. R’) C (P’.Q + R) D (P. Q + R)
Digital-Logic-Design       Boolean-Expression       APPSC-2016-DL-CS
Question 7 Explanation:
 Question 8
 A A B B C C D A, B and C
Digital-Logic-Design       Boolean-Expression       UGC-NET DEC-2019 Part-2
Question 8 Explanation:

There are 8 questions to complete.

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