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Consider the following statements associated with Boolean algebra:
1. There is nothing like subtraction or division in Boolean algebra.
2. There is possibility of having negative or fractional numbers.
3. A variable has no numerical significance.
4. Logical multiplication is same as the AND operation, and logical addition is the same as the OR operation. 5. There are only three constants within the Boolean system.
Which of the statements given above are correct?
Assertion (A): Boolean algebra and Binary number system are different from each other.
Reason (R): There are some basic operations like AND, OR and NOT which are performed in Boolean algebra.
According to De Morgan’s theorem:
1. the NOR gate is equivalent to a bubbled NAND gate.
2. individual variables can be removed form under a NOT sign, and a sum of product from can be transformed to a productof sums form.
3. the complement of the product of variables is equal to the sum of their individual complements.
4. the NAND gate is equivalent to a bubbled NOR gate.
5. individual variables can be removed from under a NOT sign, and a productofsum form can be transformed to a sumofproducts form.
Q. Which of the above statements about De Morgan’s theorem is/are not correct?
The complement of the expression is equal to
Match Listl (Boolean expressions)with Listll (Minimized expression) and select the correct answer using the codes given below the lists:
Listl
ListII
1. 0
2. B + C
3. AC +
4. AB
Codes:
A B C D
(a) 3 4 1 2
(b) 1 2 3 4
(c) 3 1 4 2
(d) 2 3 4 1
The minimized Boolean expression for the logic diagram shown below is
Assertion (A): The use of Kmaps is usually limited to sixvariables.
Reason (R): A Kmap can not be used for problems involving more than six variables.
Assertion (A): The binary number designations of the rows and columns of the Kmap are in Gray code.
Reason (R): The Gray code designation is used in Kmap to ensure that two physically adjacent squares are really adjacent i.e. their minterms or maxterms differ by only one variable.
Consider the following statements:
1. The terms which cannot be combined, further in the tabular method are called “prime implicants.’’
2. The implicants which will definitely occur in the final expression are called “essential prime implicants.”
3. The prime implicant chart is a pictorial representation of the relationships between the prime implicants and the minterms of the expression.
Which of the above statements is/are correct?
X_{8}X_{4}X_{2}X_{1 }is an 8421 BCD inputto a logic circuit whose output is 1 when X_{8} = 0, X_{4} = 0 and X_{2} = 1, or when X_{8} = 0 and X_{4} = 1. The simplest output of this logic circuit would be:
The inputs to a computer circuit are 4bits of the binary number A_{3}A_{2}A_{1}A_{0}. The circuit is required to produce 1 if and only if ail of the following conditions hold.
1. The MSB is 1 or any of the other bits are 0.
2. A_{2} is 1 or any of the other bits are 0.
3. Any of the 4bits are 0.
The minimized expression for the output of the computer circuit is
The minimum number of gate inputs required to implement the minimized output of the expression given by f are:
f = ∑m (1 ,5 , 6 , 12 , 13 , 14) + d(2, 4)
The minimized expression for the output given by:
For 4 number of variables, maximum possible self dual expressions are
For the given Venn diagram, the minimized expression for the shaded area is
For the digital circuit shown below, the output is true if majority number of inputs are false.
The Boolean expression for the output is given by:
Match Listl (Logic circuit) with Listli (Output) and select the correct answer using the codes given below the lists:
ListI
ListII
3. AB
Codes:
A B C
(a) 3 3 2
(b) 1 2 1
(c) 2 1 3
(d) 2 2 1
Match ListI (Boolean expression) with Listll (Minimized expression) and select the correct answer using the codes given below the lists:
ListI
A. A. (A + B)
B. AB + BC +
C.
D. A +
ListII
1. A + B
2. AB + C
3. A
4.
Codes:
A B C D
(a) 3 2 4 1
(b) 2 4 3 1
(c) 1 2 3 4
(d) 3 4 1 2
The minimized output equation of the Kmap shown below has
The simplified expression for the Boolean expression:
f(A, B, C, D) = ∑m (0, 2, 3, 6, 7) + ∑d (8,10,11,15) is
23 docs263 tests

23 docs263 tests
