ISRO Scientist/Engineer CS Solved Papers

Consider a pipelined processor with the following four stages
IF: Instruction Fetch
ID: Instruction Decode and Operand Fetch
EX: Execute
WB: Write Back
The IF, ID and WB stages take one clock cycle each to complete the operation. The ADD and SUB instructions need 1 clock cycle and the MUL instruction need 3 clock cycles in the EX stage. Operand forwarding is used in the pipelined processor. What is the number of clock cycles taken to complete the following sequence of instructions?

ADD R2, R1, R0 ; R2 ← R1 + R0
MUL R4, R3, R2 ; R4 ← R3 * R2
SUB R6, R5, R4 ; R6 ← R5 - R4

The use of multiple register windows with overlap causes a reduction in the number of memory accesses for
1. Function locals and parameters
2. Register saves and restores
3. Instruction fetches

A processor that has carry, overflow and sign flag bits as part of its program status word (PSW) performs addition of the following two 2's complement numbers 01001101 and 11101001. After the execution of this addition operation, the status of the carry, overflow and sign flags, respectively will be

The two numbers given below are multiplied using the Booth's algorithm.
Multiplicand: 0101 1010 1110 1110
Multiplier : 0111 0111 1011 1101
How many additions/Subtractions are required for the multiplication of the above two numbers?

The addition of 4-bit, two's complement, binary numbers 1101 and 0100 results in

Which of the flowing statements about relative addressing mode is FALSE?

Substitution of values for names (whose values are constants) is done in

A root a of equation $f(x)=0$ can be computed to any degree of accuracy if a 'good' initial approximation $x_{0}$ is chosen for which

Which of the following statement is correct

The shift operator E is defined as
E $[f(x_{i})]=f(x_{i}+h)$ and $E^{-1}[f(x_{i})]=f(x_{i}-h)$
Then $\Delta$ (forward difference) in terms of E is

The formula
$\int y(x)dx \simeq \frac{h}{2}(y_{0}+2y_{1}+......+2y_{n-1}+y_{n}) - \frac{h}{12}(\nabla y_{n}-\Delta y_{0}) - \frac{h}{24}(\nabla^{2}y_{n}+\Delta^{2}y_{0}) - \frac{19h}{720}(\nabla^{3}y_{n}-\Delta^{3}y_{0})$
is called

The cubic polynomial $y(x)$ which takes the following values:
$y(0)=1$, $y(1)=0$, $y(2)=1$ and $y(3)=10$ is,

$x=a\cos(t)$, $y=b\sin(t)$ is the parametric form of

The value of x at which y is minimum for $y=x^{2}-3x+1$ is

The formula
$P_{k}=y_{0}+k\nabla y_{0}+\frac{k(k+1)}{2}\nabla^{2}y_{0}+......+\frac{k...(k+n-1)}{n!}\nabla^{n} y_{0}$ is

If G is a graph with e edges and n vertices the sum of the degrees of all vertices in G is

Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between.

A graph in which all nodes are of equal degree, is known as

If in a graph G there is one and only one path between every pair of vertices then G is a

A simple graph (a graph without parallel edge or loops) with n vertices and k components can have at most

Consider the polynomial $p(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}$, where $a_{i}\not\equiv0, \forall i$. The minimum number of multiplications needed to evaluate p on an input x is

Consider the following code written in a pass-by-reference language like FORTRAN.

Subroutine swap (ix,iy)
It=ix
L1: ix=iy
L2: iy=it
end

ia=3
ib=8
call swap (ia,ib+5)
print , ia,ib
end

A square matrix A is called orthogonal if $A^{\prime}A=$

If two adjacent rows of a determinant are interchanged, the value of the determinant

If $\begin{vmatrix} 3 & x \\ x & 1 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix}$, then the value of x is