# Boolean Algebra · Digital Circuits · GATE ECE

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## Marks 1

GATE ECE 2024
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 _________.
GATE ECE 2022
Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.
GATE ECE 2018
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 = $$\overline A .\overline B .\ov... GATE ECE 2014 Set 2 For an n - variable Boolean function maximum number of prime implicants is GATE ECE 2014 Set 1 The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$simplifies to GATE ECE 2013 In the sum of products function f (x,y,z) =$$\sum {} $$m (2,3,4,5), the prime implicants are GATE ECE 2007 The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is GATE ECE 2006 The number of product terms in the minimized sum-of-product expression obtained through the following k-map is ( where , "d" denotes don't care states... GATE ECE 2005 The Boolean expression for the truth table shown is .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:... GATE ECE 2003 The number of distinct Boolean expressions of 4 variables is GATE ECE 1999 The Logical expression$$Y = A + \overline A B$$is equivalent to GATE ECE 1998 The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is ... GATE ECE 1998 Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the ... GATE ECE 1990 The number of Boolean functions that can be generated by n variable is equal to: ## Marks 2 GATE ECE 2017 Set 1 Which one of the following gives the simplified sum of products expression for the Boolean function$$F = {m_0} + {m_2} + {m_3} + {m_5},$$where$$F =...
GATE ECE 2016 Set 3
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 2015 Set 2
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 ...
GATE ECE 2015 Set 1
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 ...
GATE ECE 2014 Set 1
Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\o... GATE ECE 2009 If X=1 in the logic equation$$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]\left\{ {\overline X + \o...
GATE ECE 2007
The Boolean expression Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,} \overline C \,D + AB\overline ... GATE ECE 2006 The point p in the following figure is stuck- at-1. The output f will be ... GATE ECE 2004 The Boolean expression AC + B$$\overline C $$is equivalent to GATE ECE 2004 A Boolean function 'f' of two variables x and y is defined as follows: f(0,0)=f(0,1)=f(1,1)=1;f(1,0)=0 Assuming complements of x and y are not availab... GATE ECE 2003 If the functions W, X, Y and Z are as follows W= R+$$\overline P Q + \overline R $$S X =$$X = PQ\overline R \,\overline S + \overline P \,\overli...
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 B) and X(=Borrow) are
GATE ECE 1999

## Marks 10

GATE ECE 1995
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...
GATE ECE 1991
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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