Questions & Answers of Boolean algebra

Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is


The Boolean expression FX,Y,Z=X¯YZ¯+XY¯Z¯+XYZ¯+XYZ. converted into the canonical product of sum (POS) form is

A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as

F(X,Y,Z) = (1, 2, 5, 6, 7)

Which one of the product of sums given below is equal to the function F(X, Y, Z)?

The Boolean expression X+YX+Y+XY¯+X¯¯ simplifies to

Consider the Boolean function, F=w,x,y,z=wy+xy+w¯xyz+w¯ x¯y+xz+x¯y¯z¯   Which one of the following is the complete set of essential prime implicants?

For an n-variable Boolean function, the maximum number of prime implicants is

In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is

In the sum of products function f(X,Y,Z)=2,3,4,5,the prime implicants are

If X = 1 in the logic equation X+ZY¯+Z¯+XY¯X¯+Z¯X+Y=1, then

The Boolean function Y = AB + CD is to be realized using only 2-input NAND gates. The minimum number of gates required is:

The Boolean expression Y=A¯B¯C¯D+A¯BCD¯+AB¯C¯D+ABC¯D¯ can be minimized to