GATE ECE
Digital Circuits
Boolean Algebra
Previous Years Questions

## Marks 1

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$$is equivalent to The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is ... Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the ... The number of Boolean functions that can be generated by n variable is equal to: ## Marks 2 Which one of the following gives the simplified sum of products expression for the Boolean function$$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

## Marks 10

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...
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