1
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? $6$ $8$ $10$ $12$
2
Write each of these statements in the form if p, then q in English. [Hint: Refer to the list of common ways to express conditional statements] I will remember to send you the address only if you send me an e-mail message. To be a citizen of this country, it ... . It is necessary to have a valid password to log on to the server. You will reach the summit unless you begin your climb too late.
3
Suppose there are $\lceil \log n \rceil$ sorted lists of $\lfloor n /\log n \rfloor$ elements each. The time complexity of producing a sorted list of all these elements is: (Hint:Use a heap data structure) $O(n \log \log n)$ $\Theta(n \log n)$ $\Omega(n \log n)$ $\Omega\left(n^{3/2}\right)$
4
Consider the number given by the decimal expression: $16^3*9 + 16^2*7 + 16*5+3$ The number of $1’s$ in the unsigned binary representation of the number is ______
5
Consider the number given by the decimal expression: $16^3*9 + 16^2*7 + 16*5+3$ The number of $1’s$ in the unsigned binary representation of the number is ______
6
The number $43$ in $2's$ complement representation is $01010101$ $11010101$ $00101011$ $10101011$
7
The simultaneous equations on the Boolean variables $x, y, z$ and $w$, $x + y + z = 1$ $xy = 0$ $xz + w = 1$ $xy + \bar{z}\bar{w} = 0$ have the following solution for $x, y, z$ and $w,$ respectively: $0 \ 1 \ 0 \ 0$ $1 \ 1 \ 0 \ 1$ $1 \ 0 \ 1 \ 1$ $1 \ 0 \ 0 \ 0$
8
Which functions does NOT implement the Karnaugh map given below? $(w + x) y$ $xy + yw$ $(w + x) (\bar{w} + y) (\bar{x} + y)$ None of the above
9
A CPU has $24$-$bit$ instructions. A program starts at address $300$ (in decimal). Which one of the following is a legal program counter (all values in decimal)? $400$ $500$ $600$ $700$
The numbers $1, 2, .\dots n$ are inserted in a binary search tree in some order. In the resulting tree, the right subtree of the root contains $p$ nodes. The first number to be inserted in the tree must be $p$ $p + 1$ $n - p$ $n - p + 1$
We consider the addition of two $2's$ complement numbers $b_{n-1}b_{n-2}\dots b_{0}$ and $a_{n-1}a_{n-2}\dots a_{0}$. A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by $c_{n-1}c_{n-2}\dots c_{0}$ and the carry-out by $c_{out}$ ... $c_{out}\oplus c_{n-1}$ $a_{n-1}\oplus b_{n-1}\oplus c_{n-1}$