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Boolean algebra - class-XII

Description: boolean algebra
Number of Questions: 22
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Tags: electronic devices semiconductor electronics: materials, devices and simple circuits physics
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Which of the following is logically equivalent to $(p\wedge q)$ ?

  1. $p\rightarrow q$

  2. $\sim p \, \wedge \sim q$

  3. $p\, \wedge \sim q$

  4. $\sim (p\rightarrow \sim q)$


Correct Option: D

The Boolean expression $P+\overline { P } Q$, where $P$ and $Q$ are the inputs of the logic circuit, represents  

  1. AND gate

  2. NAND gate

  3. NOT gate

  4. OR gate


Correct Option: A

Person who use boolean algebra for describing the operation of logic gates first was

  1. Boole

  2. Shannon

  3. Schottky

  4. Zener


Correct Option: B
Explanation:

Person who use boolean algebra for describing the operation of logic gates first was Claude Shannon. 

In the binary number system, the number $100$ represents

  1. one

  2. three

  3. four

  4. hundred


Correct Option: C
Explanation:

In binary number system only $0$'s and $1$'s are used to built the whole number system.
Hence,
$0 = 0$
$1 = 1$
Start back at $0$ again, but add $1$ on the left,
$2 = 10$
$3 = 11$
Start back at $0$ again, and add one to the number on the left, but that number is already at $1$, so it also goes back to $0$ and $1$ is added to the next position on the left. Hence,
$4 = 100$ .... and so on.

Boolean algebra is essentially based on 

  1. symbols

  2. logic

  3. truth

  4. numbers


Correct Option: B
Explanation:

Boolean algebra is essentially based on logic. It is also known as logical algebra.

The Boolean algebra uses

  1. two digits, $0$ and $1$.

  2. two digits, $1$ and $2$.

  3. two digits, $0$ and $2$.

  4. $10$ digits, $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$.


Correct Option: A
Explanation:

The Boolean algebra uses binary number system i.e. two digits $0$ and $1$.

The value of $\bar{1}$ +$\bar{1}$  is

  1. $2$

  2. $0$

  3. $1$

  4. $10$


Correct Option: B
Explanation:

$\bar 1 + \bar 1 = 0 + 0 = 0$

What is the value of $A + \bar{A}$ in the Boolean algebra?

  1. $0$

  2. $A$

  3. $1$

  4. $\bar{A}$


Correct Option: C
Explanation:

When $A = 1,$ then $A + \bar{A} = 1 + 0 =1$
and when $A = 0$, then $A + \bar{A} = 0 + 1 = 1$

The binary number $1000$ represented by

  1. $8$

  2. $16$

  3. $32$

  4. $64$


Correct Option: A
Explanation:

$(1000) _2 = 0 \times  2^0 + 0 \times 2^1 + 0 \times 2^2 + 1 \times  2^3 = 8$

Boolean algebra is essentially based on:

  1. Numbers

  2. Symbol

  3. Logic

  4. Truth


Correct Option: C
Explanation:

Boolean algebra is based on logic.

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

  1. $A$

  2. $B$

  3. $\overline {A}$

  4. $\overline {A+B}$


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?

  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.


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?

  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


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?

  1. Commutative Law

  2. Associative Law

  3. Distributive Law

  4. All of the above


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.

  1. Associative Law

  2. Commutative Law

  3. Distributive Law

  4. Idempotent Law


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 ?

  1. 1

  2. 0

  3. Both (A) & (B)

  4. None of these


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, $A+\bar{B}=$?

  1. $B$

  2. $\bar{B}$

  3. $A$

  4. $\bar{A}$


Correct Option: C
Explanation:

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

The decimal number $16$ in binary number is

  1. $1000$

  2. $10000$

  3. $1010$

  4. $11000$


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

  1. $1101.01$

  2. $1001.01$

  3. $1001.10$

  4. $1110.010$


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

  1. $(111101) _2$

  2. $(111111) _2$

  3. $(101111) _2$

  4. $(111001) _2$


Correct Option: A
Explanation:

$100010 + 11011 = (111101) _2$

Which one of the following gives the $2's$ complement of decimal number $13$?

  1. $0010$

  2. $0011$

  3. $1100$

  4. $1101$


Correct Option: B
Explanation:

The binary representation of $13$ is $1101$. The $1's$ complement of $13$ is $0010$. The $2's$ complement of $13$ is $0010 + 1 = 0011$.

The BCD code for the character A is

  1. $1000$

  2. $1010$

  3. $1011$

  4. $1100$


Correct Option: B
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