1
GATE CSE 2003
+2
-0.6
The following is a scheme for floating point number representation using $$16$$ bits.

Let $$s, e,$$ and $$m$$ be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is

$$\left\{ {\matrix{ {{{\left( { - 1} \right)}^s}\left( {1 + m \times {2^{ - 9}}} \right){2^{e - 31}},} & {if\,the\,{\mathop{\rm exponent}\nolimits} \, \ne \,111111} \cr {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0} & {otherwise\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \cr } } \right.$$

What is the maximum difference between two successive real numbers representable in this system?

A
$${2^{ - 40}}$$
B
$${2^{ - 9}}$$
C
$${2^{ 22}}$$
D
$${2^{ 31}}$$
2
GATE CSE 2003
+1
-0.3
For a pipelined $$CPU$$ with a single $$ALU$$, consider the following situations
$$1.\,\,\,\,\,$$ The $$j+1$$ instruction uses the result of the $$j$$-$$th$$ instruction as an operand
$$2.\,\,\,\,\,$$ The execution of a conditional jump instruction
$$3.\,\,\,\,\,$$ The $$j$$-$$th$$ and $$j+1$$ instruction require the $$ALU$$ at the same time

Which of the above can cause a hazard?

A
$$1$$ and $$2$$ only
B
$$2$$ and $$3$$ only
C
$$3$$ only
D
ALL the three
3
GATE CSE 2003
+2
-0.6
Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operations take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m >= 1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is
A
n(X + Y)
B
3Y + 2X
C
n(X + Y) - X
D
Y + 2X
4
GATE CSE 2003
+2
-0.6
Consider the function f defined below.
struct item {
int data;
struct item * next;
};

int f(struct item *p) {
return ((p == NULL) || (p ->next == NULL) ||
((p->data <= p -> next -> data) &&
f(p-> next)));
}
For a given linked list p, the function f returns 1 if and only if
A
the list is empty or has exactly one element
B
the elements in the list are sorted in non-decreasing order of data value
C
the elements in the list are sorted in non-increasing order of data value
D
not all elements in the list have the same data value
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