1
GATE CSE 2012
+2
-0.6
What is the minimal form of the Karnaugh map shown below? Assume that $$X$$ denotes a don’t care term.
A
$$\overline {bd}$$
B
$$\overline {bd} + \overline {bc}$$
C
$$\overline {bd} + a\overline {bc} d$$
D
$$\overline {bd} + \overline {bc} + \overline {cd}$$
2
GATE CSE 2004
+2
-0.6
Consider a multiplexer with $$X$$ and $$Y$$ as data inputs and $$Z$$ as control input. If $$z=0$$ select input $$x,$$ and $$z=1$$ selects input $$Y$$. what are the connections required to realize the $$2-$$variable Boolean function $$f=T+R$$ without using any additional Hardware?
A
$$R$$ to $$X,$$ $$1$$ to $$Y,$$ $$T$$ to $$Z$$
B
$$T$$ to $$X,$$ $$R$$ to $$Y,$$ $$T$$ to $$Z$$
C
$$T$$ to $$X,$$ $$R$$ to $$X,$$ $$O$$ to $$Z$$
D
$$R$$ to $$X,$$ $$O$$ to $$Y,$$ $$T$$ to $$Z$$
3
GATE CSE 2003
+2
-0.6
The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of $$(xy + xz)$$ is $$4.$$ What are the minimum possible literal counts of the product -of -sum and sum -of-product representations respectively of the function given by the following Karnaugh map? Here, $$X$$ denotes “don’t care”
A
$$(11, 9)$$
B
$$(9,13)$$
C
$$(9,10)$$
D
$$(11, 11)$$
4
GATE CSE 2000
+2
-0.6
Which function does NOT implement the Karnaugh map given below?
A
$$(w+x)y$$
B
$$x\,y + y\,w$$
C
$$\left( {w + x} \right)\,\,\left( {\overline w + y} \right)\left( {\overline x + y} \right)$$
D
None of the above
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