Boolean Algebra

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 $F$ ?

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 logic circuit diagram. Which is/are the CORRECT option(s) for the output function F?

Given the following Karnaugh Map for a Boolean function F(w,x, y, z): Which one or more of the following Boolean expression(s) represent(s) F?

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

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...

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

Consider 4-variable functions f1, f2, f3, f4 expressed in sum-of-minterms form as given below. f1 = ∑(0,2,3,5,7,8,11,13) f2 = ∑(1,3,5,7,11,13, 15) f3 = ∑(0,1,4,11) f4 = ∑(0,2,6,13)...

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are sele...

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 $$\overline F$$ (co...

Which one of the following is NOT a valid identity?

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

If w, x, y, z are Boolean variables, then which one of the following is INCORRECT?

Given f(w, x, y, z) = ∑m (0,1,2,3,7,8,10) + Σd (5,6,11,15), where d represents the don't-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS)...

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...

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...

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 _______________ . $$$\left[ {D' + AB' + A'C + AC'D + A'C'D} \right]'$$$

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}...

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 $...

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

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...

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 + \overl...

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

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

$$P$$ and $$Q$$ are two propositions. Which of the following logical expressions are equivalent? $${\rm I}.$$ $${\rm P}\, \vee \sim Q$$ $${\rm I}{\rm I}.$$ $$ \sim \left( { \sim {\...

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

Let E, F and G be finite sets. Let $$X = \,\left( {E\, \cap \,F\,} \right)\, - \,\left( {F\, \cap \,G\,} \right)$$ and $$Y = \,\left( {E\, - \left( {E\, \cap \,G} \right)} \right)\...

Given two three bit number $${a_2}{a_1}{a_0}$$ and $${b_2}{b_1}{b_0}$$ and $$c,$$ the carry in the function that represents the carry generate function when these two numbers are a...

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...

$$f\left( {A,B} \right) = A' + B$$ 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,...

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

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