Boolean Algebra · Digital Circuits · GATE ECE

For the Boolean function $F(A, B, C, D) = \sum m(0,2,5,7,8,10,12,13,14,15)$, the essential prime implicants are _________.

Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.

A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by F = $$\overline A .\overline B .\ov...

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

The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to

In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are

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

The number of product terms in the minimized sum-of-product expression obtained through the following k-map is ( where , "d" denotes don't care states...

The Boolean expression for the truth table shown is .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:...

The number of distinct Boolean expressions of 4 variables is

The Logical expression $$Y = A + \overline A B$$ is equivalent to

The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is ...

Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the ...

The number of Boolean functions that can be generated by n variable is equal to:

Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ where $$F =...

Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is ...

A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$m(1,2,5,6,7) Which one of the ...

The Boolean expression F(X, Y, Z)= $$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$ converted into the canonical ...

Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\o...

If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \o...

The Boolean expression Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,} \overline C \,D + AB\overline ...

The point p in the following figure is stuck- at-1. The output f will be ...

The Boolean expression AC + B$$\overline C $$ is equivalent to

A Boolean function 'f' of two variables x and y is defined as follows: f(0,0)=f(0,1)=f(1,1)=1;f(1,0)=0 Assuming complements of x and y are not availab...

If the functions W, X, Y and Z are as follows W= R+$$\overline P Q + \overline R $$ S X = $$X = PQ\overline R \,\overline S + \overline P \,\overli...

For a binary half-subtractor having two inputs A and B, the correct set of Logical expressions for the output D(=Aminus B) and X(=Borrow) are

The minimized form of the logical expression ($$\overline A \,\overline B \,\overline C + B\overline C + \overline A B\overline C + \overline A BC ...

Given the Boolean function F in three variables R, S and T as F=$$\,\overline R \,S\overline T + R\overline {S\,} T + RST$$ (a) Express F in the mi...

In certain application, four inputs A, B, C, D (both true and complement forms available)are fed to logic circuit, producing an output F which operate...

Its is desired to generate the following three Boolean functions. $$\eqalign{ & {F_1} = a\,\overline b \,c + \overline a \,b\overline c + bc ...

A 'code converter' is to be designed to convert from the BCD(5421) to the normal BCD (8421). The input BCD combinations for each digit are below. A bl...

The four variable function f is given in terms of min-terms as: f (A B C D ) = $$\sum {} $$m (2,3,8,10,11,12,14,15 .) Using the K-map minimize the fu...