GATE ECE

Boolean Algebra

Digital Circuits

(Past Years Questions)

Marks 1

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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 = $...
GATE ECE 2018
For an n - variable Boolean function maximum number of prime implicants is
GATE ECE 2014 Set 2
The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to
GATE ECE 2014 Set 1
In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are
GATE ECE 2013
The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is
GATE ECE 2007
The number of product terms in the minimized sum-of-product expression obtained through the following k-map is ( where ,...
GATE ECE 2006
The Boolean expression for the truth table shown is .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-fam...
GATE ECE 2005
The number of distinct Boolean expressions of 4 variables is
GATE ECE 2003
The Logical expression $$Y = A + \overline A B$$ is equivalent to
GATE ECE 1999
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...
GATE ECE 1998
The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is ...
GATE ECE 1998
The number of Boolean functions that can be generated by n variable is equal to:
GATE ECE 1990

Marks 2

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Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} ...
GATE ECE 2017 Set 1
Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is ...
GATE ECE 2016 Set 3
A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$...
GATE ECE 2015 Set 2
The Boolean expression F(X, Y, Z)= $$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$ ...
GATE ECE 2015 Set 1
Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline...
GATE ECE 2014 Set 1
If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$...
GATE ECE 2009
The Boolean expression Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,} ...
GATE ECE 2007
The point p in the following figure is stuck- at-1. The output f will be ...
GATE ECE 2006
The Boolean expression AC + B$$\overline C $$ is equivalent to
GATE ECE 2004
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 compleme...
GATE ECE 2004
If the functions W, X, Y and Z are as follows W= R+$$\overline P Q + \overline R $$ S X = $$X = PQ\overline R \,\overl...
GATE ECE 2003
The minimized form of the logical expression ($$\overline A \,\overline B \,\overline C + B\overline C + \overline A B...
GATE ECE 1999
For a binary half-subtractor having two inputs A and B, the correct set of Logical expressions for the output D(=Aminus ...
GATE ECE 1999

Marks 4

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Given the Boolean function F in three variables R, S and T as F=$$\,\overline R \,S\overline T + R\overline {S\,} T + ...
GATE ECE 1996

Marks 5

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In certain application, four inputs A, B, C, D (both true and complement forms available)are fed to logic circuit, produ...
GATE ECE 1999
Its is desired to generate the following three Boolean functions. $$\eqalign{ & {F_1} = a\,\overline b \,c + \overlin...
GATE ECE 1996

Marks 10

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A 'code converter' is to be designed to convert from the BCD(5421) to the normal BCD (8421). The input BCD combinations ...
GATE ECE 1995
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 .) U...
GATE ECE 1991

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