Boolean Algebra

Consider the following 4-variable Boolean function $$ F(A, B, C, D)=\Sigma m(0,1,2,3,8,9,10,11) $$ Consider $A$ as MSB, $D$ as LSB. Which one of the following options represents the minimal sum of products form for the a...

Which one of the following options is not a property of Boolean Algebra? Note: + is OR operation, • is AND operation, and ' is NOT operation

Consider the following Boolean expression of a function $F$ : $$ F(P, Q)=(\bar{P}+Q) \oplus(\bar{P} Q) $$ Which of the following expressions is/are equivalent to $F$ ?

Consider a Boolean function $F$ with the following minterm expression: $$ F(P, Q, R, S)=\Sigma m(1,2,3,4,5,7,10,12,13,14) $$ Which of the following options is/are the minimal sum-of-products expression(s) of $F$ ?

Which of the following Boolean algebraic equation(s) is/are CORRECT?

Consider the following four variable Boolean function in sum-of-product form $$F\left(b_3, b_2, b_1, b_0\right)=\Sigma(0,2,4,8,10,11,12)$$ where the value of the function is computed by considering $b_3 b_2 b_1 b_0$ as a...

Let $X$ be a 3-variable Boolean function that produces output as ' 1 ' when at least two of the input variables are ' 1 '. Which of the following statement(s) is/are CORRECT, where $a, b, c, d, e$ are Boolean variables?

Consider a Boolean expression given by $F(X, Y, Z) = \Sigma(3,5,6,7)$. Which of the following statements is/are CORRECT?

For a Boolean variable x, which of the following statements is/are FALSE?

Consider the following Boolean expression. $$F = (X + Y + Z)(\overline X + Y)(\overline Y + Z)$$ Which of the following Boolean expressions is/are equivalent to $$\overline F$$ (complement of F)?

Consider a Boolean function f(w, x, y, z) such that f(w, 0, 0, z) = 1 f(1, x, 1, z) = x + z f(w, 1, y, z) = wz + y The number of literals in the minimal sum-of-products expression of f is ______

Which one of the following is NOT a valid identity?

What is the minimum number of 2-input NOR gates required to implement a 4-variable function function expressed in sum-of-minterms form as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements...

Consider the unsigned $$8$$-bit fixed point binary number representation below $$${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{b_3}\,\,.\,\,{b_2}\,\,{b_1}\,\,{b_0}$$$ where the position of the binary point is between $${b_3}$$ a...

Consider the minterm list form of a Boolean function 𝐹 given below. $$F\left( {P,Q,R,S} \right) = $$ $$\sum {m\left( {0,2,5,7,9,11} \right)} $$ $$ + \,\,d\left( {3,8,10,12,14} \right)$$ Here, $$m$$ denotes a minterm and...

Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

Let $$X$$ be the number of distinct $$16$$-bit integers in $$2’s$$ complement representation. Let $$Y$$ be the number of distinct $$16$$-bit integers in sign magnitude representation. Then $$X −Y$$ is ____________.

The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal representation is ____________.

Consider the Boolean operator $$ \ne $$ with the following properties: $$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \ne x = 0$$ and $$x \ne \overline x = 1.$$ Then $$x \ne y$$ is equivalent to

Let, $${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$$ where $${x_1},\,{x_2},\,{x_3},\,{x_4}$$ are Boolean Variables, and $$ \oplus $$ is the $$XOR$$ operator. Which one of the following must always be TRUE ?

The binary operator $$ \ne $$ is defined by the following truth table. p q p$$ \ne $$q 0 0 0 0 1 1 1 0 1 1 1 0 Which one of the following is true about the binary operator $$ \ne $$?

Given the function $$F = P′ + QR,$$ where $$F$$ is a function in three Boolean variables $$P,Q$$ and $$R$$ and $$P'=!P,$$ consider the following statements. $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S1} \right)\,...

Consider the equation $${\left( {43} \right)_x} = {\left( {y3} \right)_8}$$ where $$x$$ and $$y$$ are unknown. The number of possible solutions is ______________

The total number of prime implicants of the function $$f\left( {w,x,y,z} \right) = \sum {\left( {0,2,4,5,6,10} \right)} $$ _________________.

The number of min-terms after minimizing the following Boolean expression is _______________ . $$$\left[ {D' + AB' + A'C + AC'D + A'C'D} \right]'$$$

Consider the operations $$f\left( {x,y,z} \right) = X'YZ + XY' + Y'Z'$$ and $$g\left( {x,y,z} \right) = X'YZ + X'YZ' + XY$$. Which one of the following is correct?

Let $$ \ne $$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$𝑋$$ and $$𝑌$$ are Boolean variables. Consider the following two statements. $$$\eqalign{ & \left( {S1} \right)\,\,\,\,\,\,\,\left( {P \ne Q} \...

Consider the following Boolean expression for $$F:$$ $$F\left( {P,\,Q,\,R,\,S} \right) = PQ + \overline P QR + \overline P Q\overline R S.$$ The minimal sum-of-products form of $$F$$ is

The dual of a Boolean function $$F\left( {{x_1},{x_2},\,....,\,{x_n},\, + , \cdot ,'} \right),$$ written as $${F^D}$$, is the same expression as that of $$F$$ with $$+$$ and $$ \cdot $$ swapped. $$F$$ is said to be self-...

Let $$ \oplus $$ denote the exclusive $$OR\left( {XOR} \right)$$ operation. Let $$'1'$$ and $$'0'$$ denote the binary constants. Consider the following Boolean expression for $$F$$ over two variables $$P$$ and $$Q$$: $$F...

Consider the following interm expression of $$F:$$ $$F\left( {P,\,Q,\,R,\,S} \right) = \sum {0,2,5,7,8,10,13,15} $$ The minterms $$2, 7, 8$$ and $$13$$ are 'do not care' terms. The minimal sum-of-products form for $$F$$...

Which one of the following expressions does NOT represent exclusive NOR of $$x$$ and $$y?$$

The simplified $$SOP$$ (Sum of product) form of the Boolean expression $$\left( {P + \overline Q + \overline R } \right).\left( {P + \overline Q + R} \right).\left( {P + Q + \overline R } \right)$$ is

Which one of the following circuits is NOT equivalent to a $$2$$-input $$XNOR$$ (exclusive NOR ) gate

The minters expansion of $$f\left( {P,Q,R} \right) = PQ + Q\overline R + P\overline R $$ is

What is the minimum number of gates required to implement the Boolean function $$(AB+C)$$ if we have to use only $$2$$-input NOR gates?

If $$P, Q, R$$ are Boolean variables, then $$\left( {P + \overline Q } \right)$$ $$\left( {P.\overline Q + P.R} \right)\left( {\overline P .\overline R + \overline Q } \right)$$ Simplifies to

If $$P$$, $$Q$$, $$R$$ are Boolean variables, then $$(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$$ simplifies to

Consider the following Boolean function with four variables $$F\left( {w,\,x,\,y,\,z} \right) = \sum {\left( {1,\,3,\,4,\,6,\,9,\,11,\,12,\,14} \right)} $$ the function is

A circuit outputs a digit in the form of $$4$$ bits. $$0$$ is represented by $$0000$$, $$1$$ by $$0001..., $$ $$9$$ by $$1001.$$ A combinational circuit is to be designed which takes these $$4$$ bits as input and outputs...

The Boolean function $$x'y' +xy +x'y$$ is equivalent to

Which are the essential prime implicants of the following Boolean function? $$F\left( {a,b,c} \right) = {a^1}c + a{c^1} + {b^1}c$$

Express the function $$f( x, y, z)= xy'+ yz'$$ with only one complement operation and one or more $$AND/OR$$ operations. Draw the logic circuit implementing the expression obtained, using a single NOT gate and one or mor...

$$f\left( {A,B} \right) = A' + B$$ Simplified expression for function $$f((x+y,y),z)$$ is

The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$ $$$x+y+z=1$$$ $$$xy=0$$$ $$$xz+w=1$$$ $$$xy + \overline z \overline w = 0$$$ have the following for $$x, y, z$$ and $$w,$$ respectively.

Let $$f\left( {x,y,z} \right) = \overline x + \overline y x + xz$$ be a switching function. Which one of the following is valid?

Let $$^ * $$ be defined as $${x^ * }y = \overline x + y,$$ Let $$z = {x^ * }y.$$ Value of $${z^ * }x$$ is

Find the minimum sum of products form of the logic function $$f\left( {A,B,C,D} \right) = \sum d \left( {3,11,12,14} \right)$$ Where $$m$$ and $$d$$ denote the minterms and don't cares respectively.

Consider the number given by the decimal expression. $${16^3} \times 9 + {16^2} \times 7 + 16 \times 5 + 3$$ The number of $$1's$$ in the unsigned binary representation of the number is _______.

Find the minimum product of sums of the following expression $$f = ABC + \overline A \,\overline B \,\overline C .$$