1
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
$$wzy,\,wyz,\,wxz,\,\overline w xz,\,x\overline y z,\,xyz$$
2
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 $$bc'$$
3
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
4
GATE CSE 2002
Subjective
+2
-0
Transform the following logic circuit (without expressing its switching function) into an equivalent logic circuit that employs only $$6$$ $$NAND$$ gates each with $$2$$-inputs. GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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Joint Entrance Examination