Tag: digital electronics and logic gates

Questions Related to digital electronics and logic gates

If $A=1, B=0,$ then in terms of Boolean algebra , $A+\overline {B}$ equals to 

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

  1. $A$

  2. $B$

  3. $\overline {A}$

  4. $\overline {A+B}$

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Correct Option: A
Explanation:

$A=1$, $B=0$

Hence, $\bar{B}=1$
Therefore $A+\bar{B}=1+1=1=A$

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

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

  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.

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Correct Option: A,C
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.

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

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

  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

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Correct Option: A,B,C
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.

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

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

  1. Commutative Law

  2. Associative Law

  3. Distributive Law

  4. All of the above

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Correct Option: D
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:
$(A+B).(A+C)=A.A+A.C+B.A+B.C$

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

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

  1. Associative Law

  2. Commutative Law

  3. Distributive Law

  4. Idempotent Law

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Correct Option: B
Explanation:
According to the commutative Law:
$A+B=B+A$
$A.B=B.A$
Hence, it allows change in position for addition and multiplication.

What would be the output of the circuit whose boolean expression $Y=A\bar{B} +AB$ when A=1, B=0 ?

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

  1. 1

  2. 0

  3. Both (A) & (B)

  4. None of these

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Correct Option: A
Explanation:

Here,


$Y=A.\bar B+A.B$

$Y=A(B+\bar B)$

We know,

$B+\bar B= 1$

$Y=A.1=A$

When $A=1,B=0$

$Y=A=1$

Option $\textbf A$ is the correct answer

If $A=1$ and $B=0$, then in terms of Boolean algebra, $A+\bar{B}=$?

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

  1. $B$

  2. $\bar{B}$

  3. $A$

  4. $\bar{A}$

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Correct Option: C
Explanation:

$A+\bar{B}=1+0=1=A$.

The decimal number $16$ in binary number is

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  1. $1000$

  2. $10000$

  3. $1010$

  4. $11000$

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Correct Option: B
Explanation:
 2  16  
 2  8  0
 2  4  0
 2  2  0
   1  0
   0  -1

$\uparrow$ read up the remainders
So, $(16)$$ _{10}$ $= (10000)$$ _2$

The binary number of decimal number $(9.25)$$ _{10}$ is

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

  1. $1101.01$

  2. $1001.01$

  3. $1001.10$

  4. $1110.010$

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Correct Option: B
Explanation:

$(9.25) _{10} = (9) _{10} + (0.25) _{10} = (1001) _2 + (0.01) _2 = (1001.01) _2$

Sum of the two binary number $(100010) _2$ and $(11011) _2$ is

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

  1. $(111101) _2$

  2. $(111111) _2$

  3. $(101111) _2$

  4. $(111001) _2$

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Correct Option: A
Explanation:

$100010 + 11011 = (111101) _2$