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Multiple choice physics electronic devices boolean algebra digital electronics and logic gates logic gates

Which of the following is/are correctly matched to their respective statement?

  1. Distributive Law This law permits multiplying or factoring out of an expression.

  2. Double Negation Law This law allows removal of brackets from an expression and regrouping of the variables.

  3. Commutative Law The order of application of two separate terms is not important.

  4. Associative Law A term that is inverted twice is equal to the original term.
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation
According to the commutative Law,
$A+B=B+A$
$A.B=B.A$
Hence the order of application is not important.
According to the Associative Law,
$A+(B+C)=(A+B)+C$
$A.(B.C)=(A.B).C$
According to the Distributive Law,
$(A+B).(A+C)=A.A+A.C+B.A+B.C$
Hence, multiplying or factoring out is permitted.
Multiple choice physics electronic devices boolean algebra digital electronics and logic gates logic gates

Which of the following statement(s) is/are correct regarding Boolean algebra?

  1. The binary digits '$0$' and '$1$' could be used to represent 'false' and 'true' state respectively.

  2. The theory was based on the concept 'true' and 'false'

  3. In Boolean algebra only three basic operations are there namely, AND, OR , NOT

  4. In Boolean algebra, basic operations are AND, OR , NOT, NOR and NAND
Reveal answer Fill a bubble to check yourself
A,B,C Correct answer
Explanation
In Boolean algebra, the binary digits '$0$' and '$1$' could be used to represent 'false' and 'true' state respectively.
Also the operation AND, OR, NOT are the basic operations. NOR and NAND are obtainable from the combination of these basic operations.
Multiple choice physics electronic devices boolean algebra digital electronics and logic gates logic gates

Which of the following law(s) is/are included in Boolean algebra?

  1. Commutative Law

  2. Associative Law

  3. Distributive Law

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Boolean Algebra is a system of mathematics based on logic that has its own set of rules or laws which are used to define and reduce Boolean expressions.

Let $A,B,C $ be three variables.
According to the commutative Law:
$A+B=B+A$
$A.B=B.A$

According to the Associative Law:
$A+(B+C)=(A+B)+C$
$A.(B.C)=(A.B).C$

According to the Distributive Law:
$(A+B).(A+C)=A.A+A.C+B.A+B.C$
Multiple choice physics electronic devices boolean algebra digital electronics and logic gates logic gates

Fill in the blank.
The basic Laws of Boolean Algebra that relate to the _______ allowing a change in position for addition and multiplication.

  1. Associative Law

  2. Commutative Law

  3. Distributive Law

  4. Idempotent Law
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
According to the commutative Law:
$A+B=B+A$
$A.B=B.A$
Hence, it allows change in position for addition and multiplication.