1
GATE CSE 2007
+2
-0.6
Let $$f\left( {w,x,y,z} \right) = \sum {\left( {0,4,5,7,8,9,13,15} \right).}$$ Which of the following expressions are NOT equivalent to $$f?$$
$$(P)\,\,\,$$ $$x'y'z' + w'xy' + wy'z + xz$$
$$(Q)\,\,\,$$ $$w'y'z' + wx'y' + xz$$
$$(R)\,\,\,$$ $$w'y'z' + wx'y' + xyz + xy'z$$
$$(S)\,\,\,$$ $$x'y'z' + wx'y' + w'y$$
A
$$P$$ only
B
$$Q$$ and $$S$$
C
$$R$$ and $$S$$
D
$$S$$ only
2
GATE CSE 2006
+2
-0.6
Consider a Boolean function $$f(w, x, y, z).$$ Suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors $${i_1} = < {w_1},{x_1},{y_1},{z_1} >$$ and $${i_2} = < {w_2},{x_2},{y_2},{z_2} > ,$$ we would like the function to remain true as the input changes from $${i_1}$$ to $${i_2}$$ ($${i_1}$$ and $${i_2}$$ differ in exactly one bit position), without becoming false momentarily. Let $$f\left( {w,x,y,z} \right) = \sum {\left( {5,7,11,12,13,15} \right)} .$$ Which of the following cube covers of $$f$$ will entire that the required property is satisfied?
A
$$\overline w xz,\,wx\overline y ,\,x\overline y z,\,xyz,wyz$$
B
$$wxy,\,\overline w xz,\,wyz$$
C
$$wx\overline {yz} ,\,xz,\,w\overline x yz$$
D
$$wzy,\,wyz,\,wxz,\,\overline w xz,\,x\overline y z,\,xyz$$
3
GATE CSE 2004
+2
-0.6
Which are the essential prime implicants of the following Boolean function? $$F\left( {a,b,c} \right) = {a^1}c + a{c^1} + {b^1}c$$
A
$$a'c$$ and $$ac'$$
B
$$a'c$$ and $$b'c$$
C
$$a'c$$ only
D
$$ac'$$ and $$bc'$$
4
GATE CSE 2002
+2
-0.6
Consider the following logic circuit whose inputs are functions $${f_1},$$ $${f_2},$$ $${f_3},$$ and output is $$f.$$
A
$$\sum {\left( {1,4,5} \right)}$$
B
$$\sum {\left( {6,7} \right)}$$
C
$$\sum {\left( {0,1,3,5} \right)}$$
D
None of the above
GATE CSE Subjects
EXAM MAP
Medical
NEET