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?

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?

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

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