# Recent questions tagged isi2017-pcb-cs

1
Consider a simple code $\mathcal{C}$ for error detection and correction. Each codeword in $\mathcal{C}$ consists of $2$ data bits $[d_1, d_0]$ followed by check bits $[c_2, c_1, c_0]$ ... $2$ addition. Write down all the codewords for $\mathcal{C}$ Determine the minimum Hamming distance between any two distinct codewords of $\mathcal{C}$
2
Define a Boolean function $F(X_1, X_2, X_3, X_4, X_5, X_6)$ of six variables such that $\\ \begin{array}{llll} F & = & 1, & \text{when three or more input variables are at logic 1} \\ { } & = & 0, & \text{otherwise} \end{array}$ How many essential prime implicants does $F$ have? Justify they are essential.
1 vote
3
Consider a paging system with the page table stored in memory. If a memory reference takes $200$ nanoseconds, how long does a paged memory reference take? If we add a Translation Lookaside Buffer (TLB) and $75$ percent of all page-table references are TLB hits, ... effective memory reference time? Assume that finding a page-table entry in the TLB takes $20$ nanoseconds, if the entry is present.
4
Consider the following relations: $\text{STD_CHOICES } (\underline{\text{Student_ID}}, \underline{\text{Course_ID}}, \text{Semester})$ and $\text{COURSE_ASSIGN} (\underline{\text{Teacher_ID}}, \underline{\text{Course_ID}}, \underline{\text{Semester}})$. The former ... output the ID for all the students who have not been taught by the same teacher in more than one course across all semesters.
1 vote
5
Write a $C$ program to fins all permutations of a string (having at most 6 characters). For example, a string of $3$ characters like $“abc"$ has 6 possible permutations: $“abc", “acb", “bca", “bac", “cab", “cba".$
6
Show that if the edge set of the graph $G(V,E)$ with $n$ nodes can be partitioned into $2$ trees, then there is at least one vertex of degree less than $4$ in $G$.
7
Consider an alphabet $\Sigma = \{1, 2, 3\}.$ Design a deterministic finite-state automaton (DFA) that accepts all strings in $\Sigma^*$ in which the digits appear in non-decreasing sequence, from left to right. For example, the string $1123$ and $222$ would be accepted, whereas $21333$ will not be accepted.
8
Write a complete ANSI C code using recursion to calculate the $sum(s)$ of the digits of an integer number (i) consisting of maximum 5 digits. For example, (1) = if $i=12345$, then your program should print $s=15$, (2) if $i=457$, then $s=16$.
9
Let $R(A,B,C)$ be a relation with primary key $(A)$ and $S(A, D, E)$ a relation with primary key $(A, D)$. Each of the relations has $n$ tuples. If the number of tuples in $R \: \text{ natural join } S$ is $m$, then determine the number of tuples in $R$ $\text{ natural left outer join } S$.
10
A file $F$ holds the non-zero elements of two large $n \times n$ matrices, $a$ and $B$. The matrix entries are sorted as triplets $(i, j, \text{value})$, where $\text{value}$ is the $(i,j)$th element of a matrix. The file first stores the element ... ? If no, give reasons. If yes, provide a solution. Clearly explain the data structure and how you are going to store, retrieve, and add the elements.
1 vote
11
An operating system contains three resource classes. The number of resource units in these classes are $7, 7\ \text{and} \ 10$ ... state safe? Justify. If process $P_1$ now requests $(1,1,0)$ resources, then what will be the status of the new state?
Let $A=(a_1, a_2, \dots , a_n)$ be an array of $n$ distinct numbers. The array may not be sorted. The $\text{first}$ element $a_1$ is said to be a $\text{blip}$ if $a_1 > a_2$. Similarly, the $\text{last}$ element $a_n$ is said to be a $\text{blip}$ ... $O(\log n)$ time algorithm for finding a $\text{blip}$ in $A$. Justify the complexity of your algorithm.
Show that $\{1,A \bar{B}\}$ is functionality complete, i.e., any Boolean function with variables $A$ and $B$ can be expressed using these two primitives.
Write the number $(-5)^{\frac{1}{2}}$ in single precision IEEE 754 floating point form.