logic gates

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 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)...

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?

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...

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?

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

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

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 $$\left( {P + \overline Q } \right)$$ $$\left( {P.\overline Q + P.R} \right)\left( {\overline P .\overline R + \overline Q } \right)$$ Si...

In a look $$-$$ ahead carry generator, the carry generate function $${G_i}$$ and the carry propagate function $${P_i}$$ for inputs, $${A_i}$$ and $${B_i}$$ are given by: $${P_i} =...

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 tak...

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...