GATE CSE 2023
Q21.
The output of a 2-input multiplexer is connected back to one of its inputs as shown in the figure.Match the functional equivalence of this circuit to one of the following options.Q22.
A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0-X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown.Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function \bar{A}+\bar{A}\cdot \bar{C}+A\cdot \bar{B}\cdot C ?Q23.
Consider the following statements regarding the front-end and back-end of a compiler. S1: The front-end includes phases that are independent of the target hardware. S2: The back-end includes phases that are specific to the target hardware. S3: The back-end includes phases that are specific to the programming language used in the source code. Identify the CORRECT option.Q24.
A keyboard connected to a computer is used at a rate of 1 keystroke per second. The computer system polls the keyboard every 10 ms (milli seconds) to check for a keystroke and consumes 100 \mu s (micro seconds) for each poll. If it is determined after polling that a key has been pressed, the system consumes an additional 200 \mu s to process the keystroke. Let T_1 denote the fraction of a second spent in polling and processing a keystroke. In an alternative implementation, the system uses interrupts instead of polling. An interrupt is raised for every keystroke. It takes a total of 1 ms for servicing an interrupt and processing a keystroke. Let T_2 denote the fraction of a second spent in servicing the interrupt and processing a keystroke. The ratio \frac{T_1}{T_2} is ______ . (Rounded off to one decimal place)Q25.
Let SLLdel be a function that deletes a node in a singly-linked list given a pointer to the node and a pointer to the head of the list. Similarly, let DLLdel be another function that deletes a node in a doubly-linked list given a pointer to the node and a pointer to the head of the list. Let n denote the number of nodes in each of the linked lists. Which one of the following choices is TRUE about the worst-case time complexity of SLLdel and DLLdel?Q26.
Let A=\begin{bmatrix} 1 & 2 & 3 &4 \\ 4& 1& 2 &3 \\ 3& 4 & 1 &2 \\ 2 &3 &4 &1 \end{bmatrix} and B=\begin{bmatrix} 3& 4 & 1 &2 \\ 4& 1& 2 &3 \\ 1 & 2 & 3 &4 \\ 2 &3 &4 &1 \end{bmatrix}Let det(A) and det(B) denote the determinants of the matrices A and B, respectively. Which one of the options given below is TRUE?Q27.
Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.Let \lambda _1,\lambda _2,\lambda _3,\lambda _4,\; and \; \lambda _5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.The value of \lambda _1+\lambda _2+\lambda _3+ \lambda _4+ \lambda _5 = _____Q28.
A 4 kilobyte (KB) byte-addressable memory is realized using four 1 KB memory blocks. Two input address lines (IA4 and IA3) are connected to the chip select (CS) port of these memory blocks through a decoder as shown in the figure. The remaining ten input address lines from IA11-IA0 are connected to the address port of these blocks. The chip select (CS) is active high. The input memory addresses (IA11-IA0), in decimal, for the starting locations (Addr=0) of each block (indicated as X1, X2, X3, X4 in the figure) are among the options given below. Which one of the following options is CORRECT?Q29.
Consider a computer system with 57-bit virtual addressing using multi-level tree-structured page tables with L levels for virtual to physical address translation. The page size is 4 KB (1 KB = 1024 B) and a page table entry at any of the levels occupies 8 bytes. The value of L is ______.Q30.
Consider the following two-dimensional array D in the C programming language, which is stored in row-major order: int D[128][128]; Demand paging is used for allocating memory and each physical page frame holds 512 elements of the array D. The Least Recently Used (LRU) page-replacement policy is used by the operating system. A total of 30 physical page frames are allocated to a process which executes the following code snippet: for (int i = 0; i < 128; i++) for (int j = 0; j < 128; j++) D[j][i] *= 10; The number of page faults generated during the execution of this code snippet is _____.